Looks like you should be OK:

Cellular Phones:

Puerto Rico has a modern cell phone network. With one major exception, all the major US carriers are represented and offer domestic non-roaming service for US subscribers with nationwide plans. As of 2014, AT&T has the best coverage on the island, while T-Mobile runs a close second. Sprint works in some areas, but is not as reliable. Verizon phones work, displaying "Extended" without incurring roaming charges (you may have to enable data roaming to use 3G). Other CDMA carriers will also roam on Claro or Sprint. For non-US travelers, AT&T and T-Mobile are the GSM carriers; Sprint and Claro are CDMA and are probably not compatible with your phone.

(http://wikitravel.org/en/Puerto_Rico