Found a 7-pin to Component adapter that can plug into my graphics card

Can I use this with my Xbox 360 to capture video? I’ll happily provide more info if needed.

Much more information is going to be needed, but almost certainly no.

If the adapter was built for your graphics card, it’s likely a component output unless you very specifically have a card with capture capabilities (I don’t know of any combo GPU+component capture cards; I used to have an ATI card with composite capture, but I don’t think anybody continued with that combination idea). If all you know is that “it can plug in”, I’d make sure that that cable was made to work with your GPU.

I’m not sure what 7-pin connector you’re talking about (it’s probably a DIN connector, because 7 is a weird pin-count), but I recommend against plugging in random cables unless they’re specifically made to work with your card. Putting the wrong signals in the wrong places can be pretty bad for hardware. If, somehow, you’ve managed to find a card + adapter that is meant for capture, then the RCA jacks on the adapter would likely be labeled “Y-in” “PB-in” and “PR-in”, with red green and blue connectors. It’s also possible that you’re mistaking component (an HD standard) with composite (SD, with a single Yellow RCA jack for video plus white and red for the audio pair). THAT I would not be surprised to hear that you have.