JOHANNESBURG—As the global oil-price slump passed its one-year anniversary in June, Angola’s President José Eduardo dos Santos booked a trip to Beijing.

The long-serving autocrat hoped fresh loans and investment from China, Angola’s top trading partner, would buoy his country’s oil-dependent economy through choppy waters, according to financiers who do business with his government. On a weeklong visit, he signed a deal for China to build a $4.5 billion hydroelectric dam and a series of other projects.

“China...