  We study the motion of an inertial microswimmer in a non-Newtonian
environment with a finite memory and present the theoretical realization of an
unexpected transition from its random self-propulsion to rotational (circular
or elliptical) motion. Further, the rotational motion of the swimmer is
followed by spontaneous local direction reversals yet with a steady state
angular diffusion. Moreover, the advent of this behaviour is observed in the
oscillatory regime of the inertia-memory parameter space of the dynamics. We
quantify this unconventional rotational motion of microswimmer by measuring the
time evolution of direction of its instantaneous velocity or orientation. By
solving the generalized Langevin model of non-Markovian dynamics of an inertial
active Ornstein-Uhlenbeck particle, we show that the emergence of the
rotational (circular or elliptical) trajectory is due to the presence of
inertial memory in the environment or medium.
