Rep. Gabrielle Giffords, who survived a gunshot wound to the head a year ago, said Sunday she would step down from Congress this week, setting off a political scramble in Arizona to fill her seat.

In a video released on YouTube, the Democratic congresswoman said she would resign because she had more work to do on her recovery. "I'm getting better every day," said Ms. Giffords, speaking audibly but slowly. "My spirit is high."

The...