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](http://msp.org/involve/2012/5-1/p02.xhtml).)

> **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](http://129.69.211.95/pdf/mit/lcs/tm/MIT-LCS-TM-560.pdf).)