Can you join the peace corps if you are a convicted felon?

No, the Peace Corps will accept people who have been convicted of non-felony counts as long as they occurred before your 18th birthday but not felonies. However, depending on what type of felony it was, there are instances when that ban can be waived, providing the felony occurred some time ago.
The Peace Corps may accept felons depending on what the crime was. They may also choose not to accept felons if they are deemed dangerous to other members.