At 1601 GMT, the rand traded at 16.8350 against the dollar, 0.63% stronger than its previous close.
Data showed in the 12 months through December, U.S. consumer prices increased 6.5%, as expected, slowing from a rise of 7.1% in the prior month.
The dollar index, which measures the currency against six others, fell to a nearly 9-month low following the inflation reading and was last down 0.44% at 102.67.
Like most emerging market currencies, the risk-sensitive rand is highly susceptible to global drivers such as U.S. monetary policy.
Locally, investors will be digesting news of higher power bills for customers this year after South Africa's energy regulator on Thursday approved an 18.65% price rise for struggling state utility Eskom.
Eskom is implementing some of the deepest power cuts on record, of about six to eight hours a day for most households.
Shares on the Johannesburg Stock Exchange ended marginally higher, with the broader all-share index closing up 0.13%, while the top-40 index ended 0.14% higher.
The government's benchmark 2030 bond was stronger, with the yield down 5 basis points at 9.775%.
(Reporting by Anait Miridzhanian and Bhargav Acharya; Editing by Toby Chopra, Kirsten Donovan)
