A method is described for measuring small angular movements, some as small as a few tens of a picoradian, and results are presented from two applications. The method uses a linear conducting probe nominally orthogonal to the electric field in a microwave cavity. By pumping the cavity with microwave power large electric fields are generated and the linear probe detects these in a homodyne system with very high sensitivity to the angle between the field and the probe. The first application is a dc investigation of field rotation caused in a lossy waveguide by a ferrite sample and achieves a sensitivity of a few microradians. The second example is the angular rotation of electric fields in a gravitational wave detector which has a target sensitivity of picoradians and operates at 100 MHz.