At 1510 GMT, the rand weakened 1.03% to 18.3675 against the dollar.
The dollar index, which measures the U.S. currency against six major rivals, rose 0.156% to 102.64.
The rand lost over 7% against the greenback in May, but it has managed to recover those losses in June on the back of less intense power cuts by state utility Eskom.
The central bank's leading indicator for April dropped 1.0% month-on-month, falling for the fourth consecutive month this year, data showed on Tuesday.
The indicator collects data on vehicle sales, business confidence, money supply and other factors to gauge the outlook for Africa's most industrialised economy.
On the stock market, the Top-40 and the broader all-share indexes dropped around 1.6%.
South Africa's benchmark 2030 government bond was weaker, the yield up 4.5 basis points to 10.825%.
(Reporting by Tannur Anders and Anait Miridzhanian in Johannesburg; Editing by Alexander Winning and Matthew Lewis)
