Zonal geostrophic velocity fields above 1975 dbar have been estimated for the Southern Ocean from 2004 into 2011 based on sea surface topography observed by Jason altimetry and temperature/salinity measured by Argo autonomous floats. The velocity at 1000 dbar estimated with the method has been compared to Argo drift trajectory at the same pressure level available from the Asia Pacific Data Research Center (APDRC). The inferred velocities agree with those from the Argo drift within the estimated sampling error of the latter, but have fewer gaps in space and time. The velocity has also been integrated from depth to surface to determine the mean and time-variable zonal geostrophic transport in the Southern Ocean between 29.5°S and 58.5°S, primarily in the South Atlantic and South Indian Ocean basins, due to limitations in coverage of Argo. Analysis shows errors can be reduced by > 70% by averaging gridded results over wide areas. Zonal transport averaged over the entire Indian Ocean basin shows a significant correlation with the Antarctic Oscillation (AAO) at low frequencies: transport is higher than normal during a positive phase of the AAO, and lower during the negative phase.