Biden turned the ruble into rubble. Then it quickly came back.

A raft of punishing sanctions sent Russia’s currency crashing in the weeks after the invasion of Ukraine. Barely a month later, the ruble has staged a dramatic recovery — putting pressure on the Biden administration and its allies to deploy even tougher measures to undercut the Kremlin’s ability to finance the war.

The Russian currency, which was trading at about 84 rubles to the dollar on Feb. 23, the day before President Vladimir Putin launched the attack, had plunged roughly 70 percent by March 7. As of Wednesday, the ruble was...