With a 525 credit rating is it possible to be accepted for non-secured credit cards?

Yes but expect a lousy interest rate. Sometimes you will receive upfront fees (i.e. upfront annual fees and processing fees). If you are trying to build your credit history and raise your score, I recommend the following:

Start with a checking account
Maintain a good standing with the account, i.e. do not bounce checks or anything else negative because the bank will report this information to the credit bureaus. While a checking account does not really help raise a credit score (because good standing is not reported), it does establishes a credit history.

A cell phone builds credit as well as keeping you connected
Cell phone retailers pull your credit when purchasing a cell phone, if you have no credit you will not receive a cell phone. However with a little credit (which you establish with the checking account), you will qualify for a cell phone plan. Just like the checking account, the cell phone account will not dramatically raise your credit score, but it helps establishes credit history. Like wise, maintaining the account in good standing is not reported, but negative information does (i.e. not paying the bill).

Proprietary credit cards have their benefits
Apply for an easy credit card through proprietary credit cards such as gas cards, department store cards, and other cards (Gateway or Dell cards). Some of the easer department cards to get are Target, Mervynâ€™s, and JC Pennyâ€™s. Sometimes those with little to no credit can qualify for a Sears, Best Buy, or Macyâ€™s card. Maintain a good standing by not going over your credit limit and making the payments on time. Carry a balance of no more than 25% of your credit limit. You need to establish that you are making payment and not going over your credit limit. You will need to carry a balance to prove this. Proprietary cards are higher in interest (20-30%), but you need to start somewhere. View these cards as a transitional period. In other words, once your get a better rate or meaningful card (MasterCard, Visa, or AMEX) cancel the proprietary card.

Secure credit cards are useful
Apply for a secure MasterCard or Visa. In reality, secure credit cards are really debt cards. However, secure cards are reported as credit cards to the credit bureaus.

Apply for a meaningful credit card
Apply for a MasterCard or Visa credit card. Some of the easier cards to get are student based, Capital One, credit cards from your bank, Chase, and HSBC. Keep the account in good standing. Carry a balance of no more than 25% of your credit limit, do not go over your credit limit, and do not make late payments. You may only qualify for a higher APR. However, in 4-6 months call the customer service and ask for a lower APR. If you ask, you may receive. Do not get offended if they cannot give you a lower rate. You are a consumer and you can take your business to a better card. Do note that asking for a lower rate requires reviewing your account, meaning they may pull your credit. This will count as an inquiry on your credit report. Not necessarily a bad thing, but you do not want too many (removal takes 2-years).

Final word
It is hard to predict what exactly will establish your credit faster or raise your credit score better. It is best to be patient and persistant. If you find a credit card that will benefit you better, (i.e. lower rate or I an actual MasterCard or Visa) go for it. Keep in mind, you want to keep a credit card for 2-4 years in good standing to establish a good amount of credit history. You do not have to follow all of these steps. However, at the very least you will need a checking account. Every credit application asks if you have a checking and savings account. After establishing a checking account, you may want to apply for an actual credit card (i.e. Capital One) instead of following the cell phone, proprietary credit, and secure credit steps.