Depends on what you are trying to do?
For your FICO score? No. Unless your rent somehow reports to the credit bureaus which I doubt.
For a CC application? Probably not. Most just use the FICO score, but some do ask what your monthly obligations are which would include rent.
For a Mortgage? No. This is because you will be replacing the monthly rent with whatever your NEW housing payment would be, and that NEW payment will be included in your DTI when determining how much loan you will qualify for.
Hope this helps.