  We study a massless real self-interacting scalar field $\varphi$
non-minimally coupled to Einstein gravity with torsion in (2+1) space-time
dimensions in the presence of cosmological constant. The field equations with a
self-interaction potential $V(\varphi)$ including $\varphi^{n}$ terms are
derived by a variational principle. By numerically solving these field
equations with the 4th Runge-Kutta method, the circularly symmetric rotating
solutions for (2+1) dimensions Einstein gravity with torsion are obtained.
Exact analytical solutions to the field equations are derived for the proposed
metric in the absence of both torsion and angular momentum. We find that the
self-interacting potential only exists for $n=6$. We also study the motion of
massive and massless particles in (2+1) Einstein gravity with torsion coupled
to a self-interacting scalar field. The effect of torsion on the behavior of
the effective potentials of the particles is analyzed numerically.

General Relativity and Quantum Cosmology