We examine a technique that appears useful as a means of estimating the vector electric field (E) in the ionosphere with a monostatic incoherent scatter (IS) radar. The technique consists of using the altitude variation in mean Doppler velocity that is measured with an antenna beam fixed along a single line of sight. The rotation of the ion velocity vector with altitude in the E region is used to provide improved spatial and temporal resolution over other existing methods. We show that E can be extracted unambiguously from this one-beam position measurement technique when the neutral wind (U) is negligible. When U is significant, however, neither E nor U can be determined without ambiguity. Results obtained from multipulse measurements made with the Sondrestrom IS radar are used to illustrate these concepts.