  We investigate numerically light propagation in a single spiral waveguide
formed in a nonlinear photorefractive medium for a low spatial frequency of the
waveguide rotation. We present the general procedure for finding solitonic
solutions in spiral waveguiding structures, as well as the variational approach
to calculate soliton parameters analytically. Solitons supported by the spiral
waveguide perform robust stable rotational oscillatory motion, with the period
predicted by their static characteristics, without any signatures of wave
radiation or soliton decay over many rotation periods and diffraction lengths.
