Yes, you could use a TV Tuner card. Which one depends on the type of TV you watch.
For free Over-The-Air broadcast channels, you'd need a TV Tuner card that has an ATSC tuner.
For basic cable subscriptions (no cable set top box required), you'd need a TV tuner card that has a ClearQAM tuner.
For cable subscriptions that require a set top box, I'd probably recommend just using a different output from the set top box or getting a cablecard ready TV Tuner card to replace/augment your set top box.
Let us know which type of TV you watch and we'll make a recommendation.
Yes, I would be using ATSC for broadcast over the air channels. Thnx by the way for your responses.