This paper discusses the results from a simulation of a tungsten pin-cushion detector (TPCD) and its possible use as a position-sensitive gamma ray detector in the GlueX collimator system.  The design used in this study consists of eight separate tungsten plates that contain an array of tungsten pins.  When gamma rays enter the TPCD, they can produce energetic delta rays known as knock-on electrons.  The knock-on electrons leave behind an excess charge on the tungsten plate, which can be measured as a current once a connection to ground has been established.  A simulation of a TPCD was done using the physics simulation program GEANT.  The simulation tested the effectiveness of the TPCD in measuring the position of a gamma ray beam.  In the simulation, a gamma ray beam was directed at different positions on the TPCD and the variation in the current on each of the eight tungsten plates was measured.  The data from these simulations were analyzed to find beam position from tungsten plate currents.  The magnitude of the detector current was found to be on the order of several hundred pA.  The sensitivity of detector current to changes in beam position was quantified.  The simulations yielded beam position measurements that had an average error of $\pm$350 $\mu$m in a region within 3.0 cm of the beam line.  All of this suggests that the TPCD would be well suited for the active collimator system.