We describe a robust interferometer with external phase-shift control that does not require moving parts. The optical architecture resembles a common-path device in which the interfering waves propagate together in one collimated beam passing through the test sample. The collimated beam is incident on a calcite plate, which produces a polarization selective lateral translation and superposition of the reference and test waves. The characteristic features of the proposed interferometer, i.e. one-beam single-element scheme combined with external phase-shift control without moving parts, make a highly vibration insensitive device. Validation experiments are presented.