How far are we from actual test that gravity is quantum? As we all know, probing the Planck scale directly is still far beyond our current technologies. But I've heard that proving that in fact gravity is quantum should be much easier and we are not that far from this goal. To what extent is it true? If you would have to estimate, how many years it will take until we will prove experimentally that gravity is quantum? I've heard about some experiments involving entanglement of (nearly) macroscopic object which somehow would confirm that gravity is quantum. So basically I'm interested what is the most promising way to prove that gravity is quantum and how far are we from do this test?
 A: The idea that we need to perform experiments at the Planck scale to test the effect of gravity of quantum physics suffers from two potential misconceptions. The first is that the Planck scale is more than just a hypothesis. The second is that gravity can only affect quantum physics at that scale. We'll probably never be able to perform experiments that can probe the Planck scale and therefore the notion that the Planck scale is a physical scale will probably always remain a hypothesis.
However, gravity can potentially play a role at scales that are more accessible. Consider for example the idea that we can entangle two masses located at different points in space. The question is, how does the gravitation potential look like that is produce by such an entangled pair of masses? It is difficult to entangle masses that are large enough so that we can measure their gravitational potential, but it does not require us to go all the way to the Planck scale.
There are also proposals to send entangled states along paths that would experience gravity in different ways to see if that somehow effects the final state. It can be done with satellites that can prepare entangled photons. This technology already exists. So, it may not be too long before we get some feedback on this issue.
A: As other answers and comments have suggested, the question "whether gravity is quantum" is not very well-posed; it needs to be made more precise before anyone can give a fully satisfying answer to your question.
The narrow answer to your question is that gravitationally induced quantum interference effects were measured all the way back in 1975, so we've already had experimental evidence that QM responds to gravity for decades. (Some might argue that this doesn't "count", because those experiments just measured the impact of a non-dynamical background gravitational field, but in my opinion this objection suffers from the "No true Scotsman" fallacy.)
The broader answer to your question is that "whether gravity is quantum" is not a clean yes-or-no distinction. Classical general relativity and quantum mechanics are framed in terms of very different formalisms, and it isn't really logically possible that they are both exact and there's simply no more to the story. One might hope that there could be some small number of experimental findings that would prove that "gravity isn't quantum", thereby suggesting that conveniently, our current theories are the "end of the story" and no more work is needed. But this isn't the case. In fact, the opposite is true; any high-energy experimental findings that could very loosely be described as showing that gravity is "immune" to quantum effects would actually enormously complicate our physical theories, not simplify them. We'd need to very carefully map out the boundaries of these unexpected effects and then come up with some new (and probably very complicated) theory explaining the unexpected lack of cohesion between the two theories.
A: We will know how far we are from an experimental test of whether the gravitational field is quantum mechanical when such a test has been conducted.
There are proposals to test quantum mechanical effects of gravity by studying entanglement between particles in two branches of an interferometer as a result of gravitational interaction between the two particles. There is a paper called "Decoherence effects in non-classicality tests of gravity" by Rijavec et al. discussing the conditions required to do such experiments:

The numerical analysis has shown that temperatures and pressures as low as 1 K and 10−16 Pa are sufficient for generating entanglement with E = 10−2 after 0.15 s for the BM proposal and after 1.1 s for the Krisnanda proposal. Notably, cryogenic experiments can easily provide temperatures reaching 10 mK and pressures down to $10^{−16}$ Pa have already been reached in experiments with Penning traps [81]. However, the time-scale involved requires a free-falling particle to fall for 10 cm and 6.2 m respectively for the BM and the Krisnanda proposals. Clearly, maintaining the above conditions of temperature and pressure can be technically challenging. As pointed out in [10], milder environmental conditions such as $P = 10^{−15}$ Pa would lead to a decoherence time of the order of a few seconds, which is comparable to the time of the experiment. However, such conditions would invalidate the BM proposal, while the Krisnanda proposal would work only for lower temperatures ⩽10 mK. Moreover the two particles should remain aligned during the experiments, one should also prepare the system without any horizontal and vertical relative velocity, which, over time, would change the relative distance thus potentially disrupting the experiments. Table 3 compares the free-fall times and corresponding heights necessary for the two proposals at different environmental conditions. While entanglement could be difficult to generate, one could rely on other non-classical correlations such as discord [6], but this was beyond the aim of the current work.

This is an area of active research so if you want to know what's going on the best way to do that is keep an eye on the papers being published about the topic.
A: A photon from a star that is gravitationally lensed by a black hole ( a photon a long way from the black hole so few gravitons reach it) will statistically not absorb many gravitons over some  periods of time.So it will deviate from the path we expect it to follow for a while .If the photon does not absorb many more gravitons in another period of time then it will stay off the path we expect it to be on.Photons that do this to the extent that we can measure the difference in angle of arrival at a detector will be rare.But this may be one way to detect the effect of quantum gravity
A: We are 93 billion light-years close to observing gravity at the quantum scale. Please pardon my sarcasm, but I imagine the best we can do is break the standard model of particle physics and make nomologically consistent models of quantum gravity.
