Welcome to FlyerTalk. Using miles or points to upgrade a paid ticket is determined by the rules of the frequent flyer program of the airline operating the flights. How you earned those miles or points (e.g. by flying, or through a credit card) is not important.
If you primarily fly one airline you should understand their mileage upgrade requirements, then look for a credit card which works with their program. Be aware that few airlines offer upgrades from the lowest price economy class tickets, most require purchase of a more expensive ticket or a money co-payment in conjunction with the mileage upgrade.
If you fly various airlines you should look for a card with the largest number of airline transfer partners. In order these would be:
- Starwood Preferred Guest (credit cards issued by American Express)
- American Express Membership Rewards
- Diners Club Rewards (not accepting applications for new personal accounts in Canada or USA)
- Chase Ultimate Rewards