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StrayCats, the catalog of NuSTAR stray light observations, contains data from bright X-ray sources that fall within crowded source regions. These observations offer unique additional data with which to monitor sources like X-ray binaries that show variable timing behavior. In this work, we present a timing analysis of stray light data of the high mass X-ray binary SMC X-1, the first scientific analysis of a single source from the StrayCats project. We describe the process of screening stray light data for scientific analysis, verify the orbital ephemeris, and create both time and energy resolved pulse profiles. We find that the orbital ephemeris of SMC X-1 is unchanged and confirm a long-term spin up rate of $\dot{\nu}=(2.52\pm0.03)\times10^{-11}$ Hz s$^{-1}$. We also note that the shape of SMC X-1's pulse profile, while remaining double-peaked, varies significantly with time and only slightly with energy.