  We construct metrics of positive scalar curvature on manifolds with circle
actions. One of our main results is that there exist $S^1$-invariant metrics of
positive scalar curvature on every $S^1$-manifold which has a fixed point
component of codimension 2. As a consequence we can prove that there are
non-invariant metrics of positive scalar curvature on many manifolds with
circle actions. Results from equivariant bordism allow us to show that there is
an invariant metric of positive scalar curvature on the connected sum of two
copies of a simply connected semi-free $S^1$-manifold $M$ of dimension at least
six provided that $M$ is not $\text{spin}$ or that $M$ is $\text{spin}$ and the
$S^1$-action is of odd type. If $M$ is spin and the $S^1$-action of even type
then there is a $k>0$ such that the equivariant connected sum of $2^k$ copies
of $M$ admits an invariant metric of positive scalar curvature if and only if a
generalized $\hat{A}$-genus of $M/S^1$ vanishes.
