The emission from low-mass X-ray binaries (LMXBs) arises from the accretion of mass onto a neutron star or black hole. A knowledge of the amount of mass being accreted as well as changes in this value are therefore essential inputs into models of these systems. Despite the need for this information, we currently lack an easily applied method that allows the accretion rate to be measured. X-ray color-color plots and UV observations can be used for this purpose, but these methods require access to oversubscribed satellites. Even if time is granted on these facilities, there is no guarantee that the source will be in a desired state when the observations take place. In this paper we show that an estimate of the ratio of the mass accretion rate to the Eddington rate can be obtained for Sco X-1 by using the Johnson B magnitude. Based on correlated X-ray and ground-based observations, we find that for Sco X-1, M˙/M˙E=-(0.123+/-0.007)B+2.543+/-0.085. This relation is valid when the system is on its normal and lower flaring branches. Based on theoretical models, we suggest that similar relations should also exist for other LMXBs.