I'm not sure I have the syntax correct as I don't want to open Access and find out, but the idea is that you use the DatePart function in Access. You can compare parts of dates with it. Try something like:
SELECT * FROM BIRTHDAY_TABLE
WHERE DatePart ("m", [BDAY_FIELD]) = DatePart("m",Date()) AND
DatePart("d",[BDAY_FIELD]) = DatePart("d",Date())
(There might be a DatePart arg that allows comparison for month and day without the year in a single comparison)