  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 non-axisymmetric 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 integation 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
{\mu}Hz/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.
