Following a recent proposal by S. B. Zheng and G. C. Guo [Phys. Rev. Lett. 85, 2392 (2000)], we report an experiment in which two Rydberg atoms crossing a nonresonant cavity are entangled by coherent energy exchange. The process, mediated by the virtual emission and absorption of a microwave photon, is characterized by a collision mixing angle 4 orders of magnitude larger than for atoms colliding in free space with the same impact parameter. The final entangled state is controlled by adjusting the atom-cavity detuning. This procedure, essentially insensitive to thermal fields and to photon decay, opens promising perspectives for complex entanglement manipulations.