"To do a burnout" is 烧胎, so I assume a reasonable sentence would be:
昨天晚上我在停车场烧胎。
How would one distinguish this activity from piling up tyres and setting fire to them, for example in this news clipping:
[Pupils] had been unable to go to school ... because roads were being blocked with stones and burning tyres.
The problem was not that people were doing burnouts on the road to school.
TL;DR
昨晚我的车在停车场烧胎了。