The object of the present paper is to study 3-dimensional trans-Sasakian manifolds admitting Ricci solitons and gradient Ricci solitons. We prove that if $(g,V,\lambda)$ is a Ricci soliton where $V$ is collinear with the characteristic vector field $\xi$, then $V$ is a constant multiple of $\xi$ and the manifold is of constant scalar curvature provided $\alpha,\beta={}$constant. Next we prove that in a 3-dimensional trans-Sasakian manifold with constant scalar curvature if $g$ is a gradient Ricci soliton, then the manifold is either a $\beta$-Kenmotsu manifold or an Einstein manifold. As a consequence of this result we obtain several corollaries.