Try creating a calculated field and with something like this for the formula:
// Take the difference between the actual date and the date truncated
// to the first day of the quarter. Add one so the range is 1-92.
DATEDIFF('day', DATETRUNC('quarter',[Order Date]), [Order Date]) + 1
You'll want to replace [Order Date] with your actual date dimension. You probably want to convert this calculation to a dimension when you are done with it, since you don't want to do any aggregation on it.
Austin, thanks very much. This worked brilliantly.