Welcome to the forum!
Let me make sure I understand. Do you actually want the card to be shaped like that? Or you want that shape as part of the contents of the card (along with the text and phone numbers and all)?
Well, either way, I can get you started. There are 2 ways to produce that shape with vector paths. In this case, either way is pretty easy.
I would say that if you are using Inkscape for this project, as a one time thing, I would suggest Path menu > Trace Bitmap. It's an auto-trace engine, which in this case will reproduce that PNG very faithfully, very quickly. If this is just your first project with Inkscape, and you plan more projects in the future, it's probably a good idea to start learning how to use the Pen/Bezier tool. And this simple path will be a great introduction.
I'm hesitating to give instructions for both, since I don't know which way you would choose. But I'll give you links to the manual where you can begin to become familiar with whatever you choose. Once you let us know which way you want to go, I can refer you to other materials (tutorials and such) and also make some additional comments to get you going.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Trace.htmlhttp://tavmjong.free.fr/INKSCAPE/MANUAL/html/Paths-Creating.html#Paths-Bezier