Can you connect rainwater pipes to a septic tank?

No. It would be a violation of most building and health codes.

Why would you want to? Why not buy a water tank and catch the rain water for other uses.

The water from a moderate to heavy rain will exceed the capacity of the septic tank. It could cause sewage to backup into the home. It could also cause sewage to backup out of the rainwater pipes. The extra water will upset the micro-environment that the bacteria need to process the waste. You may end up with a smelly tank.

Too much water may send unprocessed waste into the absorption field pipes and clog them. This would be veryexpensive to fix. Clogged pipes in the absorption field cannot be repaired. The only solutions are: (1) a new absorption field (if there is room on the property); or (2) a personal sewage treatment plant.

You would be liable for any damage caused to neighboring properties. Moreover, some jurisdictions provide criminal penalties for anyone that modifies a septic system in such a manner that it could contaminate water downstream.