At 0740 GMT, the rouble was 0.4% weaker against the dollar at 64.62. Versus the euro, the Russian currency had lost 0.4% to trade at 71.64.
Trump said he would impose a 10% tariff on $300 billion of Chinese imports from Sept. 1, jolting financial markets.
Moody's said the new tariffs would weigh on the global economy at a time when growth is slowing in the United States, China and the euro zone
Trump's move sparked a sell-off on emerging markets on Thursday with investors piling into safe-haven assets.
"The rouble is exposed to external volatility through the recently increased long positioning of international investors in Russian local assets (debt mostly)," VTB Capital analysts said.
U.S. media reports late on Thursday said Trump had signed an executive order imposing sanctions on Russia over the poisoning of a former Russian spy in southern England last year.
The sanctions rhetoric posed additional risks to the rouble, said Mikhail Poddubsky, an analyst at Promsvyazbank.
Prices for oil, Russia's main export, rose on Friday, paring losses after an overnight plunge.
Brent crude oil was up 2% at $61.7 a barrel.
The dollar-denominated RTS index was down 2.5% to 1,313 points. The rouble-based MOEX Russian index was 1.3% lower at 2,692 points.