I can't think of a way to do it automatically. There is DATEDIFF in a calculation but you can't use TODAY as an option. It needs to be a date on the object.
If you have to have it and don't mind a manually process, here is my recommendation:
Create a date custom field called something like Date for PTO Accural
Create a calculated custom field called Day of Year where the equation is DATEDIFF(Date for PTO Accrual,"1/1/2016")
Every day, just do a bulk edit of your users where you change the Date for PTO Accural
Not fun as you have to update it every day, but is the best I could come up with.
And actually, if you are going to bulk edit, it might be easier to just bulk edit the day of the year anyway. So maybe this isn't the best option.
Hopefully this will trigger something for someone else and they will come up with a better idea for you. 😉