The GlueX experiment at Jefferson lab will use gamma rays to excite protons in hopes of producing mesons with unusual J$^{PC}$ numbers, which are called exotic mesons. Observation of exotic mesons will help to confirm the standard model of the strong nuclear force known as QCD. To accurately filter the meson spectrum it will be necessary to use linearly polarized gamma rays. In the GlueX experiment, polarized gamma rays will be produced by collimating a beam of photons created through the coherent bremsstrahlung effect. \par In order to maximize the effectiveness of collimation it will be necessary to position the collimator approximately 75 m from the beam source. The large distance between beam source and collimator and the small aperture of the collimator pose a difficultly in reliably centering the beam on the collimator aperture. With proper positioning the amount of energy deposited in the collimator can be kept to a minimum, which reduces secondary particle showering and maximizes the amount of beam flux reaching the experimental target. \par The need for precise positioning of the gamma ray beam in GlueX will make the use of a position-sensitive gamma ray monitor necessary. The monitor will have to provide a real-time measurement of the beam position accurate to within a fraction of a millimeter. The simplest design of a position-sensitive detector involves using heavy metals to convert a fraction of the incident gamma rays into a secondary particle shower. The electromagnetic shower creates a net charge on the metal, and if connected to ground, this excess charge can be recorded as a current. If the metal is divided into plates, the induced current in each plate will have a sensitive dependence on the gamma ray beam power and position. Once calibrated, this simple detector can be used as a beam position monitor. The magnitude of the induced current is sensitive to detector geometry, and so finding the ideal detector geometry can reduce the cost of data acquisition equipment and improve accuracy. \par A team at SLAC\cite{mw74} has developed a detector geometry to solve a similar problem. The SLAC team has designed a position-sensitive detector that uses tungsten pins as a radiator, which they call the Tungsten Pin Cushion Detector or TPCD. The SLAC detector geometry consists of four arrays of tungsten pins fixed onto four tungsten base plates. The pin geometry of the detector increases the surface area of the tungsten radiator, which increases the emission of knock-ons produced in an electromagnetic shower. The excess charge on these tungsten ``pin-cushions" creates a current, the magnitude of which is related to the beam's position and intensity. \par This paper investigates the possibility of using a modified version of the SLAC TPCD as a position detector for the gamma ray beam in the GlueX experiment using a GEANT simulation. The simulations test the sensitivity of the detector to changes in beam position and are analyzed to predict beam position for given detector currents.