Let's say I have some document which is printed on both sides. I need scanned copy of both sides. I have already got the front part of it and need the back of it now. Can I say --> send me a scanned copy of "rear of the card" ?
A card has two faces: front and back.
You would say
Send me a scanned copy of the back of the card
This phrasing could work if copies of both sides are needed:
Send me a scanned copy of your ID (recto + verso)
More about recto and verso can be found here.