You either need a 'based on' airman's certificate under FAR 61.75 or a one-off validation, which means getting a licence verification from your CAA and a visit to the local FSDO.
The certificate needs a current flight review with a CFI to be valid (1 hr flying + 1 hr ground review). You also need a US visa that permits entry and exit by private aircraft; VWP won't do.
You will also need to process the export with CBP at your port of exit from the US. Best to use a local agent to process the paperwork and smooth the process. It's relatively cheap to do so.