We develop a method to infer the upstream solar wind pressure at Mars using data from the Mars Global Surveyor (MGS) magnetometer instrument. The method assumes magnetic field pressure in the magnetic pileup region balances the incident solar wind dynamic pressure. Newtonian pressure balance conditions are imposed for positions off of the subflow point. Proof of concept exists from the mapping phase of the spacecraft mission, when the orbital geometry at a constant altitude allows fits to magnetic field data as a function of solar zenith angle. During the elliptical orbit phase of MGS, when the spacecraft passes through a large range of altitudes, such fits are not possible. However, the measured magnetic pressure in the magnetic pileup region is scaled by the same means as derived for the mapping orbits and reasonable upstream solar wind pressure is obtained. We compare the distribution of solar wind pressure calculated using MGS data with the solar wind pressure measured upstream of the Earth during the same time period and find good agreement, further supporting this algorithm as a valid proxy for the incident solar wind pressure. The response of the position of the Magnetic Pileup Boundary to the inferred solar wind pressure also validates the method. High solar wind ram pressure depresses the altitude of the Magnetic Pileup Boundary.