Is it possible? In the sense that it cannot logically be proven to be impossible, perhaps.
But practically speaking, it does not seem to be possible at all. Certainly our knowledge of physics and neurology does not predict that such an ability would exist. Ostensible demonstrations of psychokinesis (PK) have not risen above those that could equally well be reproduced by amateur magicians, so there is little reason to believe they are legitimate. Regardless, some researchers have tried to establish the existence of PK anyway by performing statistical experiments with random number generators (see the Rhine Institute, or Princeton's PEAR project). However, the results generated by these research teams are at best described as debatable, at worst described as pathological science.
That brings me to your 2nd question regarding any theories for PK. No, there are none (no scientifically valid ones, that is), and that is one of those warning sings that you're dealing with more of a pseudoscience than anything else. A theory starts with a valid scientific hypothesis that is tested and confirmed by repeated experiments by independent research teams, and anything less is not a theory. However, parapsychologists have not even got this far. Because our present scientific knowledge does not predict the existence of PK, it's impossible to form a valid hypothesis for it other than the trivial "PK exists". But this is an orphaned superficial hypothesis completely separated from any sound foundation in known science. That's a great example of how science does NOT proceed. Science is a process which builds upon itself, and here is a good example where the results are being presumed first with no supporting theoretical foundation. As U of O psychology professor Ray Hyman said of remote viewing research, "you need a positive theory to guide you as to what needs to be controlled, and what can be ignored. Parapsychologists have not come close to this as yet."