The gang broke into the compound of the National Construction College in Kings Norton late on Sunday night and used the JCB digger to force open gates of the site.
The thieves then tried to get away in the digger but were spotted by a passing West Mercia Police patrol car.
The gang rammed the marked police car before jumping into a Land Rover Defender that had been following in convoy.
Both police officers were uninjured in the collision. The JCB was left blocking the road with the engine still running.
Detective Inspector Jim Foy from Birmingham South CID said: “The gang are known to have climbed a fence and then used the digger to smash through gates at the college and use main roads to try and get away in the JCB.
“When they spotted the police car the thieves then rammed the police vehicle, which could well have caused serious injury.
“Thankfully the West Mercia officers were not hurt, but the combination of the heavy plant vehicle and the weather conditions could well have resulted in a far more serious collision.
“The thieves escaped in a Land Rover Defender than was running in tandem with the stolen JCB and we appeal for anyone in the area who might have seen that type of 4×4, which is fairly uncommon, last night to contact police.”