I do not know if there is any GraphQL plugin or asset specific to Godot, but you may be able to use an existing GraphQL library with Godot through C# or GDNative.
On this Reddit post, a user asked a similar question and got some answers that may be helpful to look at. It seems the user got much the same advice, being suggested to use C# and an existing GraphQL library written for C#.
It looks like there isn't a GDScript asset to interface with GraphQL, at least not as far as I can tell.