Record yourself singing the song a cappella (which means no musical accompaniment, just your voice). The rendition must be no longer than 90 seconds. The booking agent wants to know you can sing the song, not that you can sing it in five octaves.
Call the team's main switchboard number and ask them to connect you with the person who handles bookings for the national anthem. Sometimes they are called the talent coordinators, sometimes the booking agent, and sometimes they don't have an official name. Be persistent and keep calling until you find someone who can direct you to the correct person.
Burn a CD with your anthem rendition. Mail it and a cover letter that includes all of your contact information to the appropriate person. Send it certified mail with a return receipt to verify that it arrived. Include your name, phone number, and email address in the letter and on the CD in case the two get separated.
Wait two weeks before following up with a phone call. After that first follow-up call, do not continue to call. If they like your rendition, they will be in touch with possible dates.
If you are asked to sing, remember to dress respectfully. No shredded jeans, no teensy skirts and no strapless anything. If you are a female, avoid heels. They tend to sink into the infield, making it hard to walk.