Police from the Banbridge, Craigavon and Armagh district took to social media to post pictures of the incident and to warn road users of the dangers of drinking and driving.
They say the driver was located by officers.
"B Section on tonight. Imagine our surprise in Armagh, a motorist set fire to their car after they crashed it,” a PSNI spokesperson said.
"The good news is we found the driver and they will be told after a sobering night in the cells that their car is a write off. Don’t drink and drive.”