We report on single-crystal rubrene field-effect transistors (FETs) with ferromagnetic Co electrodes, tunnel-coupled to the conduction channel via an Al2O3 tunnel barrier. Magnetic and electronic characterization shows that the Al2O3 film not only protects the Co from undesired oxidation, but also provides a highly controlled tunnel barrier for overcoming the conductivity mismatch problem when injecting spins from a ferromagnetic metal into a semiconductor. Our FETs provide a significant step towards the realization of a device that integrates FET and spin-valve functionality, one of the major goals of spintronics.