Yes, not only is this allowable it is probably foolish not to do so with the way this world works. Truth is, if a SAHM one day finds herself alone, say widowed, and she has no credit history she will not be able to get any loans for anything while she waits for life insurance to be paid out etc. How would she feed her kids or keep a roof over their heads?
While I am not an advocate of credit cards in general it would be foolish to say they do not serve a purpose. Credit cards prove to the world you are financially responsible. Get a few and use them sparingly, as in you could make a purchase at
Walmart with a credit card and pay it off in the next transaction with the cash in your hand. It used to be store cards were the easiest to get so I suspect they still are, just be patient and build yourself a history one month at a time. After a while move to a bank card or an American Express.