Looking at the link JPJP posted it says "Licenses FAA CPL ATP" which as bafanguy says will limit the number of applicants.
If you don't have a FAA ATP Mesa will send you to a CTP class which must be completed before attempting the ATP written.
In the FAA world there are no conversion exams unless you hold a Canadian license. Everyone else goes through the same process Americans go through - the CTP, the written exam, a training program and a checkride.