We present one of the first studies in which interferometric synthetic aperture radar (InSAR) data from the Shuttle Radar Topography Mission (SRTM) are analyzed with regard to the detectability of ocean surface current variations. The InSAR system of SRTM was designed for high-resolution topographic mapping, using two SAR antennas on a Space Shuttle with a cross-track separation of 60 m. For technical reasons, there was an additional along-track antenna separation of 7 m, which results in a time lag of about 0.5 ms between the acquisitions of images by the two antennas. In theory, this time lag causes additional phase differences, which are proportional to the line-of-sight velocity of moving targets and can thus be exploited, to some extent, for measuring oceanic currents. Indeed, some SRTM images acquired over water exhibit clear signatures of typical flow patterns. We show an example of an X-band phase image of the Dutch Waddenzee and discuss the plausibility of interpreting it in terms of sea surface height or current variations or the effect of waves. We find that only currents can be responsible for phase variations of the observed magnitude on spatial scales of a few 100 meters. We convert the data into a surface current field, which is found to be consistent with the theoretical current field at the time of the SRTM overflight according to a current atlas. Based on this encouraging result and theoretical findings, we discuss the general potential of SAR interferometry from space for oceanic applications.