  We show that the "twisted" planar random walk - which results by summing up
stationary increments rotated by multiples of a fixed angle - is recurrent
under diverse assumptions on the increment process. For example, if the
increment process is alpha-mixing and of finite second moment, then the twisted
random walk is recurrent for every angle fixed choice of the angle out of a set
of full Lebesgue measure, no matter how slow the mixing coefficients decay.
