I was thinking and came up with the question "Can the path of a photon be warped by a strong magnetic field?" I tried searching online for an answer but couldn't find much scientific evidence of it being possible or not.
So is it possible?
No. It is not possible without some complicated interactions with matter.
Maxwell's equations are linear. Which means that the superposition of two solutions is another solution. Physically,this means that if you have a laser beam traveling along, and you put a strong magnetic field in its path... the resulting field will be the laser + the magnetic field, with no change at all in the laser. The two are superimposed with no change.
If you have matter, it's a different story. The matter is already vibrating/doing its thing due to the laser, and the added magnetic field can change the properties of the matter, which changes how it reacts to the laser, etc.
NB this is just a footnote to NeuroFuzzy's answer, and you should accept his answer not this one.
NeuroFuzzy says a magnetic field cannot bend light and I agree but ...
An electromagnetic field of sufficiently high strength will cause spacetime curvature. For magnetic fields this isn't a simple issue, as discussed in Does strong magnetic field cause time dilation?, because in practice you cannot separate electric and magnetic fields. However given that anything capable of generating a very strong magnetic field will cause curvature that means light rays will not follow straight lines.
If axions exist then in a sufficiently strong magnetic field photons can convert into axions, and this affects the propagation of the light. The CAST experiment is looking for exactly this penomenon. My recollection is that a few years back it looked as an effect had been detected, though it was later dismissed as a systematic error.
Both of these are vanshingly small effects (if they exist at all in the case of axions) and they don't invalidate NeuroFuzzy's answer. Still, it's these sorts of esoteric phenomena that make physics fun.
The similar to questions of the form "What is the charge of the photon?", "How do photons interact with electrons [if they have no charge]", and so on. A "photon" is a relatively complicated notion, as it lies somewhere in between the small wave description (it's supposed to be a plane wave, otherwise it's not an eigenstate) and the large scale point description (because usually we want a photon of finite radius).
A photon is just a wave of oscillating electric and magnetic fields, and since electric and magnetic fields combine linearly, they will not interact. Consider a long slinky. A photon would be a standing wave: a persistent, oscillating wave. (Or, if you want, if my slinky is a mile long, the photon might be just 10 meters of steady wave travelling one way.) An outside magnetic field would then be like holding the entire slinky up a few feet, or the slinky sagging in a parabola from its own weight. These will change the "shape" of the photon locally, but the photon is still a photon and consists of the same relative local changes. And once the photon or the magnetic field is gone, the other one is unaffected.
That light combines linearly like this lets a lot of cool things happen, indeed. As a example where this doesn't work, water waves, especially small ones, are pretty nonlinear: if I have one wave rippling along, it can look pretty different depending on whether the surface is on a large scale sloping up or down (the "external field"). For instance, little ripples act differently if they're going up or down the side of a marge larger wave.
In a conventional way, no. But it can. As said by @NeuroFuzzy and @Alex Meiburg, a photon doesn't interact with a magnetic field by means of eletromagnetic force, so at first sigth the photon path can't be bent. But a strong magnetic field, as imposed by the OP, can warp the spacetime because it contributes to the stress-energy tensor, and therefore bend a photon's path as predicted by Einstein's equations. To see more, go to https://en.m.wikipedia.org/wiki/Einstein_field_equations#Einstein.E2.80.93Maxwell_equations where the proper contribution of the eletromagnetic field for the stress-energy tensor is shown