Same problem here: We know the Turkish Law but not the US law. So, to
answer your question we need more details: What's "American Statute of
Frauds" about? What exactly is "wrighting a contract" especially what are
the prerequisites and consequences of this practise according to US law.
If you provide us with more details about these in your law system, it will
give us clues about exactly what you're asking and help us to compare
the systems.