At 1540 GMT, the rand traded at 17.2850 against the dollar, 2.4% weaker than its previous close.
The dollar index, which measures the U.S. dollar against six rivals, was up 0.902% at 105.15.
The risk-sensitive rand often takes its cues from global drivers such as the U.S. monetary policy in the absence of major local events.
The S&P Global South Africa PMI survey showed on Thursday that activity in the private sector expanded in December but at a slower pace than in November as high prices and power cuts depressed client demand.
On the Johannesburg stock market, the Top-40 and the broader all-share ended over 1% higher.
The government's benchmark 2030 bond was weaker in afternoon deals, with the yield up 5 basis points to 10.060%.
(Reporting by Bhargav Acharya and Anait MiridzhanianEditing by Vinay Dwivedi and Barbara Lewis)