Can I get my Apple Pencil repaired?

The only serviceable component of an Apple Pencil is the user-replaceable Pencil Tip - these being available from Apple in a pack of four:

Apple Pencil Tips - 4 pack - Apple

Otherwise, if your Apple Pencil is damaged, the only option is complete replacement.

I'm afraid, unless your Apple Pencil is still covered by a warranty, there is no service option for this accessory.