How do I 2D scan a shape and import to Tinkercad

I'm trying to take a basic 2D shape and scan it, convert it to .svg and import into Tinkercad. I first tried scanning as a .pdf and converting, but all Tinkercad sees is the 8.5x11 shape. Next I tried scanning as a .jpg, but it imports a distorted 3D shape.

Is there a simple way to scan with a basic desktop scanner in a format that Tinkercad will import properly?

The first sequence you performed created a raster image, not a vector image. You need to use an intermediate program to convert the scan to vector. A great free program for that purpose, one I've used often, is Inkscape. The Trace Bitmap feature will present a few options. For beginning conversions, leave the defaults as is.

If you want to go a bit farther, grab Paths to OpenSCAD extension for Inkscape, and OpenSCAD, of course. Once you convert to vector, you can generate OpenSCAD code and create an STL directly from OpenSCAD.

You'll get more accurate results with your scanner. If you don't need precision, even a photograph can be used.