A study of the dc Josephson current between two superconducting leads in thepresence of a precessing classical spin is presented. The precession gives rise to a time-dependenttunnel potential which not only creates different tunneling probabilities for spin-up and spin-down quasiparticles, but also introduces a time-dependent spin-flip term. In particular, westudy the effects of the spin-flip term alone on the Josephson current between two spin-singletsuperconductors as a function of precession frequency and junction transparency. The systemdisplays a steady-state solution although the magnitude and nature of the current is indeedaffected by the precession frequency of the classical spin.