[en] The gyrokinetic collision algorithm of Xu and Rosenbluth based on the formalism of Catto and Tsang has been extended and implemented in a partially linearized gyrokinetic simulation code. Both drag and diffusion contributions to the collision operator are retained. This extends the work of Xu and Rosenbluth by including momentum and energy-conserving source terms and by removing the restriction to a single Fourier mode. The scheme approximately conserves energy and momentum locally in a statistical sense. Test cases demonstrating the accuracy of the collision operator and code timings are presented. The additional cost of doing collisions is an acceptably small fraction of the cost of pushing the ions. The implementation of the collision algorithm is first-order accurate in time, which proves to be adequate for weak collisions. As part of using the ion-temperature-gradient (ITG) instability as a test case, the linear dispersion relation for an ITG mode in the local limit with weak collisions has been derived from the formalism of Chang and Callen. The authors have checked this calculation with an alternative derivation based on an extension of the Hammett-Perkins Landau-fluid model in which both viscosity and thermal conductivity are used to fit the results of a Fokker-Planck kinetic theory. The effect of collisions on the ITG mode at long wavelengths is to increase the linear growth rate and lower the threshold value of the ratio of density to temperature scale lengths. The particle simulations generally confirm the dependence of the growth rate on collisionality and show that the momentum and energy-conserving source terms need to be retained. The ion thermal transport accompanying the ITG instability is increased by collisions. Their experience so far is that the collisional model ceases to be reliable when the collisionality becomes too strong