We propose an Aharonov-Bohm interferometer with a quantum dot molecule embedded in one arm and study the spin-dependent transport due to the interplay of the Fano and Rashba effects. It is found that the Fano resonances of the molecular states exhibit opposite directions of asymmetric tails with one being from peak to dip and the other from dip to peak. The Rashba spin-orbit interaction induces a spin-dependent phase, making the two Fano dips overlap for one spin component of conductance and the two Fano peaks overlap for the other spin component. Both the direction and magnitude of the spin polarization of the conductance are easily controlled and manipulated through the Rashba parameter and interdot coupling strength. In addition, spin accumulations with opposite signs can be generated in the two quantum dots.