Right-angle wiggling (RAW) electron paramagnetic resonance (EPR) spectroscopy is introduced. In this two-dimensional pulse EPR technique the orientation of the external magnetic field B-0 is varied during the pulse sequence. For this purpose an additional sinusoidal field of variable amplitude DeltaB(0)(perpendicular to) is applied perpendicular to the orientation of B-0. RAW-EPR is an alternative and experimentally much less demanding technique to right-angle spinning for performing anisotropy-resolved EPR experiments [Sierra and Schweiger, Mol. Phys. 95, 973 (1998)]. It can be applied to improve the resolution of EPR spectra of orientationally disordered systems or to separate overlapping single-crystal EPR spectra, and to facilitate an unambiguous interpretation of these spectra. A detailed theoretical description of RAW-EPR is given. Model calculations for systems with axial and orthorhombic symmetry, as well as a number of RAW-EPR experiments on paramagnetic systems with anisotropic interactions are presented.