Your credit is calculated not only by having a credit card, but by your age, years of employment, property owned, months or years in your apartment/rent, bank history, debts, bankruptcy and more. Not paying rent? Bad idea. Please look for the advice of an attorney.
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First of all, I wouldn't assume you don't have a credit record. I would check your credit using the AnnualCreditReport.com website which is free and see for yourself.
More specifically, I'm not sure that rent is an extension of credit and therefore may not be eligible to be reported on your credit report. Additionally, utilities and land based phones are also not usually reported, however cell phone bills are.
In any case, having seen multiple credit reports, I have never seen an account relating to a person's rent.
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