Can I deduct unpaid amount of a loan I gave to a friend who is in no position to pay it back?

It depends. You may be able to claim it as a personal bad debt.

The IRS warns: For a bad debt, you must show that at the time of the transaction you intended to make a loan and not a gift. If you lend money to a relative or friend with the understanding the relative or friend may not repay it, you must consider it as a gift and not as a loan, and you may not deduct it as a bad debt."

It would be helpful, if you got audited, to have something in writing.

To show that a debt is worthless, you must establish that you've taken reasonable steps to collect the debt. It's not necessary to go to court if you can show that a judgment from the court would be uncollectible. You may take the deduction only in the year the debt becomes worthless. You don't have to wait until a debt is due to determine that it's worthless.

See: Topic No. 453 Bad Debt Deduction.