Hi Dixied. This may not be the job for your son. The first thing I thought is that a person who has no car should not be looking for work in a field that requires you provide your own transportation. Unfortunately, not having transportation is a consequences of the poor choices he has made in life. I hope you think long and hard about rescue-ing him.
Personally, knowing what I know about addicts and recovery, I would not give a person in a half-way house a car. Just my opinion. But in all honesty, recovering addicts don't need to be traveling around town in a car all day by themselves. It would be a huge trigger to most. Having a car is downfall to many addicts straight out of recovery.
Unfortunately your son may be angry if you don't support him in this, but where he is now and the situation he is in is his responsibility not yours. And solving his transportation problem likewise, be his responsibility, not yours.
Maybe just use the old fall back, "youre a smart boy. I know you'll figure out a solution to this on your own."