A hash to curve function H, mapping bit strings to points on an elliptic curve, is often required in cryptographic schemes based on elliptic curves. Its construction is based on a deterministic encoding and a cryptographic hash function, which complementarily dominate its execution time. To improve the performance of $H$, we propose a parallel strategy where two units execute in tandem the internal operations of $H$. We instantiate this approach with a parallel software implementation of a hash to curve function that outputs points on a twisted Edwards curve. A performance benchmark on Haswell and Skylake micro-architectures shows that our parallel implementation is 1.4 times faster than its sequential implementation.