How long does it take a slight compression fracture in t12 to recover?

About 3 months. It takes about 3 months to heal, though total healing may take 6 months or more. It is a process. Smoking, some drugs (non steroidal anti-inflammatory medications like ibuprofen, aspirin, naproxen) can slow the process.
Usually within 12. Weeks. However, one should get evaluated as to any bone density loss and aggressively treat if present to minimize risk of another fracture if due to bone density issues. Sometimes this may be a sign of other diseases so make sure you have an evaluation by your physician.

Related Questions

I fell off my m'bike. I have compression fracture t12 vertebra (25% loss of height) how long will it take to heal? The Thai doctor said three weeks.

About right. Assuming you are healthy and a non-smoker that is a reasonable timeframe. Could take up to 6 weeks. Avoid high impact activities or heavy lifting.
Compression fracture. A compression fracture with a 25% loss in height is not insignificant, I would think the healing time might be a bit longer than three weeks, more likely closer to 2-3 months based on your age of 39 years old.