Currently the textbox card doesn't support a border color. The closest you could come is changing the background on the card on a dashboard but that's the entire card.
If you're wanting just a border I'd recommend adding this to the Idea Exchange.
As an alternative, you can use the HTML Single Value Brick. This would allow you to create a border with some basic HTML and CSS. You can find this brick in the Appstore by searching for brick.
