  We report the coherent coupling of two electron spins at a distance via
virtual microwave photons. Each spin is trapped in a silicon double quantum dot
at either end of a superconducting resonator, achieving spin-photon couplings
up to around $g_s/2\pi = 40 \ \text{MHz}$. As the two spins are brought into
resonance with each other, but detuned from the photons, an avoided crossing
larger than the spin linewidths is observed with an exchange splitting around
$2J/2\pi = 20 \ \text{MHz}$. In addition, photon-number states are resolved
from the shift $2\chi_s/2\pi = -13 \ \text{MHz}$ that they induce on the spin
frequency. These observations demonstrate that we reach the strong dispersive
regime of circuit quantum electrodynamics with spins. Achieving spin-spin
coupling without real photons is essential to long-range two-qubit gates
between spin qubits and scalable networks of spin qubits on a chip.
