Yes it means "to compensate" but your example is incorrect. IT should say "I will make it up to him for my bad behaviour". Another example-" THe show was cancelled,so to make up for it they gave us free tickets to another show".

It doesn't quite work like that. You can say 'His kindness and good manners make up for his bad behaviour'. or 'He took his wife out for an extremely expensive meal to make up for forgetting their wedding anniversary' If you want to include the person you are compensating - the 'him' in your example - you can use the expression 'make it up to someone'. For example: 'I'm sorry about xx. I'll make it up to you later, I promise'.