Yes, it is possible to trap a single light ray in a polygon.
Mitchell, Zachary, Gregory Simon, and Xueying Zhao. "Trapping light rays aperiodically with mirrors." Involve, a Journal of Mathematics 5.1 (2012): 9-14. (Journal link.)
Abstract. We construct a configuration of disjoint segment mirrors in the plane that traps a single light ray aperiodically, providing a negative solution to a conjecture of O’Rourke and Petrovici. We expand this to show that any finite number of rays from a source can be trapped aperiodically.
To obtain a polygon, one would have to connect their disjoint segments into a path, but I think this would not be difficult.
But it is not possible to trap light rays from a continuum of directions:
Dawson, RJ MacG, B. E. McDonald, J. Mycielski, and L. Pachter. "Light Traps." (1996). (PDF download.)