We calculate H$alpha$-based star formation rates and determine the star formation rate-stellar mass relation for members of three SpARCS clusters at $z sim 1.6$ and serendipitously identified field galaxies at similar redshifts to the clusters. We find similar star formation rates in cluster and field galaxies throughout our range of stellar masses. The results are comparable to those seen in other clusters at similar redshifts, and consistent with our previous photometric evidence for little quenching activity in clusters. One possible explanation for our results is that galaxies in our $z sim 1.6$ clusters have been accreted too recently to show signs of environmental quenching. It is also possible that the clusters are not yet dynamically mature enough to produce important environmental quenching effects shown to be important at low redshift, such as ram pressure stripping or harassment.