The way in which an international student is selected for an athletic scholarship is similar to the screening process that local US high school athletes have to go through.
A scholarship aspirant can contact a college coach by phone, email and by sending personal recruiting packets. If you are looking to contact by phone, then skype is a good option as international calls can be expensive.
Like local students, international scholarship students should start the recruiting process early. You should not delay the process until the later parts of your senior year. It takes more time to recruit an international athlete, and you also need to provide evidence of your abilities in the form of recruiting tapes as well other information needed by coaches to make a decision. These things take some time. The good news is that coaches in the US regularly provide international student scholarships to athletes.
International athletes are present in numbers in sports like Soccer, Hockey and increasingly in Baseball as well. High School students from certain territories also need to take SAT or ACT and provide their result to the NCAA Clearinghouse, similar to a US student. Remember that you cannot get admission on the basis of your performance in TOEFL and TWSE if you want an athletic scholarship or if you are looking to join the NCAA Division One or TWO.
The fact that you are not a well-known athlete has both advantages and disadvantages. The advantage of being new is that you can get recruited easily after you approach the selecting authority because there is no danger of you being a player for whom the recruiter has to compete with other colleges.
When you approach a foreign coach, you will have to tell them what you are capable of and will you be worth the investment. The disadvantage of being an unknown is that coaches have to assess your performance against the opposition you play and work out more logistics compared to when they recruit a national player. However, you can overcome this situation; what you need to do is start the process well in advance and be aggressive when contacting schools.
International student scholarships for athletes can enable you to continue on in your field of interest. So, if you are planning to further your career as an athlete in a particular field and you are willing to relocate to another country, you may consider applying for an athletic scholarship.