Stable polarization-locked temporal vector solitons are found in a saturable absorber mode-locked fiber laser with weak cavity birefringence. The system is theoretically modeled with two coupled complex GinzburgLandau equations that include fiber birefringence, spectral filtering, saturable gain, and slow saturable absorption. The solutions to this system are similar to those for elliptically polarized vector solitons in a lossless birefringent fiber. Numerical simulations show qualitative agreement with experimental results.