For example, ones with free frequent flyer miles upon registration, or maybe some of the Amazon.com credit cards?
My credit card applications keep on getting rejected.
For the record, I'm an incoming PhD student on a fellowship with an expected annual income of $30k for the next 5 years. I wanted to apply for reward cards since some of them were available and I wanted to try them out (but I'm ignorant of the bigger picture as I know little about credit cards).
Reward cards are for people who can demonstrate to the lender that paying them the rewards is "worth it", and the lender comes ahead in the end.
Let me step back from just answering your question and understand what you are trying to do.
First, stop doing what you are doing right now. No further applications as you have reduced your chances of getting unsecured credit by having a lot of hard hits to your report.
I assume you have a SSN, and in that case what you are doing is digging a deep hole to put yourself into the next year unless you have a job at hand (to justify a debt-income ratio that a lender will look at before approval).
Read this and ask questions: Ways to establish credit history for international student
Tell us more about your background: esp. if you have a job, how much credit you are seeking and what made you decide applying for rewards cards was a good idea to begin with.
Updated after OPs edit:
Your question has been answered already: the answer being "Yes". I trust the answer and the person behind it.
However, I know where you are coming from, and what you should focus on is establish a strong foundation for your credit. In that light you shouldn't be asking about rewards card.
Rewards will come (I am told) but the time's not now. The reason is embedded in your own edit:
For the record, I'm an incoming PhD student on a fellowship with an expected annual income of $30k for the next 5 years. I wanted to apply for reward cards since some of them were available and I wanted to try them out (but I'm ignorant of the bigger picture as I know little about credit cards)
The lenders have no metric about your expected annual income: they can see the data in a W2, in a 1040 or similar.
Anything else is up for speculation; even your expected salary on a contract: if your project gets shelved or your advisor gets fired, you no longer have the money. If the lender gives you a line of credit you are then likely to use it up and then have a hard time paying it back.
Establish strong foundation for your credit, focus your efforts there for now.
If you have done less than 3 apps recently, see if you get a secured credit card.
If you don't get approved, it looks like you can have your parents to help you out? Add yourself as an authorized user to a BofA card they own. I know BofA reports the authorized users on their cards.
You can try a student credit union: I use http://www.schoolsfirstfcu.org/. They rock. The fact that my professors also have accounts there and I often go in with them when I have a favor to ask from the CU might bias my feedback, so do your own research.
You are a smart guy, put that brain to use :-D
Best of luck!
Reward cards are usually (not necessarily) offered to people with excellent (735+) credit. By keeping applying and getting rejected you're only lowering your chances as your credit score gets lower because of the applications.
So the answer to your question is yes. As a rule, free, rewards and premium credit cards would be harder to get approved for than cards with fees and without rewards.
As an actual solution to your problem, you might want to consider Capital One's lineup of rewards cards. You can see that some are listed for people of average credit (note these have more onerous terms though), and you can get a preapproval without impacting your credit score.
If that still doesn't work you can/should
1.) Check your credit score to make sure it is where you would expect it to be, and there is nothing wrong negatively impacting it.
2.) Find a secured card.
3.) There are other ways to improve your credit score, but I won't list them all as I don't know anything about your situation.
