How many laps around a acre to make a mile?

By modern definition, an acre can have any shape as long as it is 4,840 square yards, which means that the answer of your question depends on the shape of the area.

However, traditionally an acre was a rectangle with a length of 1/8 mile and a width of 1/80 mile, which means the perimeter was 22/80 mile. So roughly 3.6 laps around it would make a mile.