How soon soon would you like the status, what do you want from the status, and how much credit card spend do you do per (month or year) average that you could steer to this/these card(s)?

The reason for these followup quesitons is that the answer is often "yes, but unless you have high spending all the time it may not be a good way to do it".

For example, Priority Club gives you Gold status at 20k points no matter how you earn them, and Platinum status at 60k points no matter how you earn them. But to earn them through a credit card, you've got to put many tens of thousands of dollars on it. On the other hand, if you go to the Priority Club forum and pay attention to the "bonus offers" sticky, you'll find that there are so many promos you can register for that run concurrently that many people get Gold status after just a few nights and Platinum status after less than a dozen stays early in the year (even at inexpensive properties), so what's the point of wiating until you've spend tens of thousands of dollars to do it by credit card spending? And Platinum at Priority Club gets you even more points (so free stays quickly), but is not as reliable at upgrades as, say HHonors Gold, and does not get you free breakfast and other similar perks the way HHonors Gold. But OTOH HHonors runs (untargeted) promos very rarely, so if that's the program you want, the credit card route might be relatively better there.

If you live somewhere where AA works for you as well as any other airline, then I'd say that's the long term holy grail, because it's the only airline where you can get lifetime elite status through any kind of mileage earning (including credit cards). And once you earn them, you can even use them for things like hotel stays (if you don't need all those miles for flights), since it's how many miles you earned, not your balance, that matters toward lifetime status. But it doesn't earn you any status (if you're not qualifying by flying) at all until you get to 1 million lifetime earned miles, at which point you're suddenly AAdvantage Gold for life.

By the way, the way to earn miles through credit cards at AA is not to use one (unless you've got a lot of credit card spend a year, as in six digits at least), but rather to "churn" them. Unlike Chase, Citi still allows churning, and allows you to apply for 2 cards every 60 days, and right now lots of cards give 15k to 25k bonuses for $250 to $750 in purchases during the first few months, with first year annual fee waived. So apply, purchase, cancel, lather, repeat, and you get way more miles than you'd ever get from spending alone if you only have five digits of spending you can put on a card per year.

Completely opposite is United, where you can "pre-buy" status for a year by paying a lot up front, and then what you've paid up front can be used to pay for flights for the rest of the year. But if you only want inexpensive domestic flights, you're likely to lose a lot on this.

Finally, bear this in mind: Status is fairly usless on an airline you're not going to fly much, or at a hotel chain you're not going to stay in much. And there are other ways to "bootstrap yourself" into status, like Challenges at AA, and status match at some other airlines or some hotel chains. Few credit cards will get you status quickly.

And remember, with the exception of lifetime status, all status has to be requalified for every year, with limited exceptions like "soft landings" (drop only one status level a year) at some programs. So if it takes you much more than a year of credit card use to get enough points to earn status, that may not help you consistently!