The U.S. oil-rig count rose by 12 to 640 in the latest week, according to Baker Hughes Inc., breaking 29 straight weeks of decline.

The number of U.S. oil-drilling rigs, which is a proxy for activity in the oil industry, has fallen sharply since oil prices headed south last year. Oil prices plummeted nearly 60% from June 2014 to a six-year low in March as soaring production from the U.S. and other countries overwhelmed global demand. The swoon caught many oil traders, industry executives and policy makers off guard and rattled...