Sounds like an XR250. It would not be a direct swap like The
Dirt Rat was, I don't think. That doesn't mean it's not do-able, but it may not be as 'simple' as The
Dirt Rat was.
If you can get it for free or close to free, I say go for it. Worst case scenario is you'd have to make some mounts and deal with mounting an exhaust.
Again I say go for it, but only if the bike is close to free.
A new motor is $450. By the time you add in tires, side covers, eBay header, chain, battery, and sundries you're looking at maybe $750. You may be able to save some money if you can get a wrecked CB donor bike to get a motor from. You'd also get the wiring for the CDI, RR etc.
Any more than that you can find an XR200 that already rides, but without the new motor.
I really did like building and riding The
Dirt Rat.