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Joseph O'Rourke
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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.)

Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958