Detection jitter quantifies variance introduced by the detector in the determination of photon arrival time. It is a crucial performance parameter for systems using superconducting nanowire single photon detectors (SNSPDs). In this work, we have demonstrated that the detection timing jitter is limited in part by the spatial variation of the photon detection events along the length of the wire. We define this jitter source as a geometric jitter since it is related to the length and area of the SNSPD. To characterize the geometric jitter, we have constructed a differential cryogenic readout with less than 7 ps of an electronic jitter that can amplify the pulses generated from the two ends of an SNSPD. By differencing the measured arrival times of the two electrical pulses, we were able to partially cancel out the difference of the propagation times and thus reduce the uncertainty of the photon arrival time. We proved that the variation of the differential propagation time was a few ps for a 3 μm × 3 μm device, while it increased up to 50 ps for a 20 μm × 20 μm device. In a 20 μm × 20 μm large SNSPD, we achieved a 20% reduction in the overall detection timing jitter for detecting the telecom-wavelength photons by using the differential cryogenic readout.