This question explains how energy curves spacetime. But I would like to know why energy curves spacetime, is there something like particle interaction that produce this result?
"Why" is never a good answerable question in physics. Physics likes much more questions like "how".
Consider, for example, that once there will be an answer for that, explaining for example, some complex interaction between the graviton field and all other. Actually, also this will be a "how" answer. From that point, you will be able to ask again, "Why the graviton field interacts on this way?"
On the phenomenologist view, it isn't even task of the physics, to answer "why" questions. It has only to describe the phenomena of the Universe in a clear framework. Others don't agree that. For example, from the phenomenologist view, it would be enough to describe, how the galactic rotation curves differ from their calculated values. There won't be needed to search for dark matter particles or some fifth interaction.
In my opinion, the chains of the "why" questions, as in my example, is infinite, and every "how" answer what the physics gives for them, allows us to step further in this chain.
For your specific question, even this next step doesn't exist yet. The best what we have currently, is an experimentally well validated "how" (the General Relativity).
If you agree that matter curves spacetime, then energy is no different, since we know from lots of other things that E = $mc^2$, and that's why energy also curves it.
If you need to know why anything curves spacetime, eg matter (and by corollary energy), then it is simply that because of the equivalence principle particle trajectories simply are determined by the spacetime, not any of the particle's properties (except if zero mass then light like). We know this from many measurements. That is then the simplest explanation, and the predictions and evidence from it at energy levels accessible so far have confirmed it.
If we ever come up with a successful theory of quantum gravity (eg, in the still unproven string or superstring or M theory, it requires that there be a graviton that couples to all mass energy, and thus GR in the classical limit - no way to have a string theory otherwise, i.e., it requires a spin 2 particle which couples to all) that is backed up, maybe we'll know why it couples to any matter energy the same way. There is no other why, but we need that quantum gravity theory for any deeper explanation
The best answer is simply that that's the way general relativity works. If you believe $E = mc^2$ then you can see that if mass causes space to curve, then so does energy. If we ever find a theory of quantum gravity, it is likely that we will be able to describe this interaction using gravitons.