Offence and offense are two spellings of the same noun. The spelling depends on the type of English.
In British English, “offence” is the normal spelling, so it’s take offence.
In American English, “offense” is standard, so it’s take offense.
The same distinction applies to similar words, such as defence or defense, licence or license, and pretence or pretense.
It’s important to choose one spelling and use it consistently. The QuillBot Grammar Checker can help you with this.