Yes, store credit cards are generally available even for bad credit. Sometimes you have even better options with unsecured regular credit cards.
Lets assume, your credit score is in hight 500's, then your best bet will be Capital One QuicksilverOne or Capital One Platinum cards
If your score is in mid 500's you can apply for Credit One Bank® Platinum Visa® for Building Credit, or a Milestone Gold credit card.
Greater access to credit than before - $700 credit limit
Get a Mastercard accepted online, in store and in app
Account history is reported to the three major credit bureaus in the U.S.
$0 liability for unauthorized use
Access your account online or from your mobile device 24/7
Among store cards JC Penney's is the one that can probably approve you with a score in low 500's.