Gradual solar energetic particle (SEP) events are known to be correlated with coronal mass ejections (CMEs) and soft X-ray flares. The current paradigm of particle acceleration in these events attributes it to CME-driven shock waves in the solar corona and in interplanetary space. Even in small gradual SEP events related to CMEs with speeds in the (possibly submagnetosonic) range of 300-800 km s-1, shock waves at global coronal scales, as evidenced by associated metric type II radio bursts, are important. Recent observational evidence from soft X-ray imaging data supports models of coronal shock wave propagation in the solar atmosphere as freely propagating blast waves that refract toward the solar surface as they propagate away from the flare site. Based on these observations, we study a model of test-particle acceleration in such a global refracting coronal shock wave. Such shocks may also be generated by solar eruptions other than flares, e.g., slow CMEs. The geometry of the shock wave results in the observer in the interplanetary medium being magnetically connected with the downstream region of the shock wave. Thus, steady-state diffusive shock acceleration predicts that the energy spectrum of the escaping ions is a power law, as typically observed—a result that is not obtained naturally if the observer is connected to the upstream region of the shock wave. Using parameters of upstream turbulence obtained from models of a cyclotron-heated solar corona, we calculate typical timescales of diffusive proton acceleration and show them to be consistent with the maximum proton energies typically observed in small, gradual SEP events. Acceleration in refracting coronal shock waves may also provide a preacceleration mechanism for further acceleration in CME-driven shocks in large gradual SEP events.