Shifts in Southern Ocean (SO, $40 - 85^{o}S$) shortwave cloud feedback ($SW_{FB}$) toward more positive values are the dominant contributor to higher effective climate sensitivity (ECS) in Coupled Model Intercomparison Project phase 6 (CMIP6) models. To provide an observational constraint on the SO $SW_{FB}$, we use a simplified physical model to connect SO $SW_{FB}$ with the response of column-integrated liquid water mass (LWP) to warming and the susceptibility of albedo to LWP in 50 CMIP5 and CMIP6 GCMs. In turn, we predict the responses of SO LWP using a cloud-controlling factor (CCF) model. The combination of the CCF model and radiative susceptibility explains about $50$\% of the variance in the GCM-simulated $SW_{FB}$ in the SO. Observations of SW radiation fluxes, LWP, and CCFs from reanalysis are used to constrain the SO $SW_{FB}$. The response of SO LWP to warming is constrained to $2.76\ -\ 4.19$ $g\ m^{-2}\ K^{-1}$, relative to a GCM prior of $0.64\ -\ 9.33$ $g\ m^{-2}\ K^{-1}$. The susceptibility of albedo to LWP is constrained to be $0.43\ -\ 0.90$ $ (kg\ m^{-2})^{-1}$, relative to $0.30\ -\ 3.91$ $(kg\ m^{-2})^{-1}$. The overall constraint on the contribution of SO to global mean $SW_{FB}$ is $-0.168\ -\ 0.051$ $W\ m^{-2}\ K^{-1}$, relative to $-0.277\ -\ 0.270$ $ W m^{-2} K^{-1}$. In summary, observations suggest SO $SW_{FB}$ is less likely to be as extremely positive as predicted by some CMIP6 GCMs, but more likely to range from moderate negative to weakly positive.