The LIGO's discovery of binary black hole mergers has opened up a new era of transient gravitational wave astronomy. The potential detection of gravitational radiation from another class of astronomical objects, rapidly spinning nonaxisymmetric neutron stars, would constitute a new area of gravitational wave astronomy. Scorpius X-1 (Sco X-1) is one of the most promising sources of continuous gravitational radiation to be detected with present-generation ground-based gravitational wave detectors, such as Advanced LIGO and Advanced Virgo. As the sensitivity of these detectors improve in the coming years, so will power of the search algorithms being used to find gravitational wave signals. Those searches will still require integration over nearly year long observational spans to detect the incredibly weak signals from rotating neutron stars. For low mass X-ray binaries such as Sco X-1 this difficult task is compounded by neutron star "spin wandering" caused by stochastic accretion fluctuations. In this paper, we analyze X-ray data from the RXTE satellite to infer the fluctuating torque on the neutron star in Sco X-1. We then perform a large-scale simulation to quantify the statistical properties of spin-wandering effects on the gravitational wave signal frequency and phase evolution. We find that there are a broad range of expected maximum levels of frequency wandering corresponding to maximum drifts of between 0.3-50 μHz/sec over a year at 99% confidence. These results can be cast in terms of the maximum allowed length of a coherent signal model neglecting spin-wandering effects as ranging between 5-80 days. This study is designed to guide the development and evaluation of Sco X-1 search algorithms. © 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.