I'll take care of the problem.
Is''ci penso io il problema''a correct way of saying''I'll take care of the
No. You should have been able to tell by the pronoun “ci” that the verb “pensare” requires an indirect object, not a direct object (otherwise it would be “lo penso io”), so it should be “al problema,” not “il problema.”
However, “ci penso io” already means what you are trying to say, so just leave it at that.