You can rent a car using a secured credit card, because secured lines of credit work the same way as a normal credit card and are reported as such. The difference between a secured and unsecured card is the secured card has a security deposit against the line in case of default. The creditor does not touch the security deposit -- in fact it is in a bank account so it can grow with interest -- until the borrower defaults on his balance.
Car rental companies almost always take a card from one of the major issuers, such as Visa, MasterCard and Discover, but any other brand of credit card is a dicey proposition. Thus it is better to apply for a secured credit card co-branded with a major payment network. Also, the secured account must have enough available credit to equal the estimated charges for the rental -- called a blocking charge. This could be a problem with a secured card, because some only come with a limit of a few hundred dollars or the amount of collateral you put down.
Before trying to use a secured card to acquire a rental, ask the customer service representative if the company puts a temporary charge on the card until the car is returned and how much. Compare that to your credit line. If the blocking on the card exceeds the available limit, the credit card payment network will decline the card.
When the blocking hold required by the rental company exceeds your limit, consider downgrading to a cheaper rental or ask about other options. Some rental companies allow renters to use a debit card linked to a checking account in lieu of a credit card. A few might even agree to cash. Also, you can pay with a different payment method once you return the car. Request the company remove the blocking charge from the secured account if you want to pay with an alternative method.