Your wording was a bit ambiguous. Could you please clarify: Is itch.io blocking access to their site through Iranian IPs or is Iran blocking the site itch.io? Because if it's the latter, you are asking for help at the wrong place.
Blocking an entire country would be something that sites rarely ever do and they would only do so if there was a very pressing reason. (Like regular denial-of-service attacks on the site itself from that IP range, or constant attempts to gain access to other user's accounts, or a stream of spam in the forums that was too much for the moderators to put up with on a daily basis, ... Stuff like that.)
Also: Have you tried the (free) Tor browser? Because if that works for you, you might be able to save the money for a paid VPN (assuming you use one).
I hope any of this helps.