No, there shouldn't be a comma there. This is how you should punctuate your message:
"Sorry I haven't written for so long. I was very busy with revising for my exams."
There is no comma because the first sentence is a shortened version of 'I'm sorry that I haven't written for so long'. If the rest of the sentence explains WHAT you are sorry about, you shouldn't use a comma.
If the rest of the sentence is simply an explanation, you need some form of punctuation after 'Sorry':
"You haven't written in ages!"
"Sorry! I've been busy revising for my exams."