This question is not so simple.
For example, if the birthday is June 1.
If the current date is May 1, 2017, then it should be 30 days.
If the current date is June 2, 2017, then it should be 364 days. Instead of 1 day.
To process only the month, it is OK to add a string to the current year.
select DATEDIFF (day, convert (datetime, substring (convert (varchar, getdate (), 112), 1,4) + substring ('20000101', 5, len ('20000101')), 112), getdate ())