How can an international MRO apply for FAA approval?
These 14 CFR Part 145 Forms might be the forms you are looking for however there may be other forms for applying from overseas. 

This site (FAA Aircraft Repair Stations Homepage) has some good links and here are the pre application regulations you need to comply with. 

Here is the letter of the law of the FAA regulations (Starts at Title 14 Section 145.1). 

I am no lawyer and cant really comment on this but I have no idea how FAA regulations work outside of the country and how/what foreign entities must comply with. I would advise contacting a local lawyer as well as a US lawyer about this.