[en] A semi-implicit orbit-averaged time-integration algorithm has been successfully implemented in a gyrokinetic particle simulation code for the study of self-consistent phenomena in a strongly magnetized plasma. The semi-implicit aspect of the integration scheme relaxes the timestep constraints required to ensure numerical stability. The orbit averaging is useful in reducing statistical noise and relaxes the statistical constraints for kinetic simulation. For appropriate applications, the semi-implicit orbit-averaged algorithm should be more efficient than are traditional particle-in-cell plasma simulation algorithms with explicit time-integration schemes. Both a linear numerical dispersion analysis and illustrative simulation examples are presented. 12 refs., 10 figs