We present the complete differential decay rates for the process B_s -> J/psi K^+ K^- including S-wave and P-wave angular momentum states for the K^+ K^- meson pair. We examine the effect of an S-wave component on the determination of the CP violating phase 2beta_s. Data from the B-factories indicate that an S-wave component of about 10% may be expected in the phi(1020) resonance region. We find that if this contribution is ignored in the analysis it could cause a bias in the measured value of 2beta_s towards zero of the order of 10%. When including the K^+K^- S-wave component we observe an increase in the statistical error on 2beta_s by less than 15%. We also point out the possibility of measuring the sign of cos2beta_s by using the interference between the K^+K^- S-wave and P-wave amplitudes to resolve the strong phase ambiguity. We conclude that the S-wave component can be properly taken into account in the analysis.