Can I change the shape of an uploaded image?

An image will always be uploaded as a rectangle but you can use this method to cover an image so only a circle of it is showing. 
First you will need to have a graphic file with a circle transparency above the image field for upload.  You can do this by uploading the circle transparency as a masked object. So, you would upload the master pdf without the circle transparency. You would set in acrobat two form fields, one for the circle transparency and the other for the photo that the customer is going to upload.

To create the masked image, create a layered photoshop file with the center area transparent. This PSD file should not have the background layer so you can see the transparency. Save the photoshop file as a PDF preserving transparency. Newer versions of Photoshop may not have a Preserve Transparency option showing in the save dialogs. The transparent portions of the image will show a checkered background when viewing in Photoshop, the transparent areas should not show as white.

You will upload this frame PDF in the image upload area for the template.  In the Field Setup area for the template in the "Field Type" tab set this to graphic file and "Data for this field will come from:" should be set to graphic file.  In the "Data Capture" tab select the circle transparency PDF file you uploaded. Make sure to use the Stacking Order option so the image the customer uploads is set below the layer the circle transparency is set to.