At 0728 GMT, the rand traded at 14.8520 versus the dollar, around 0.2% stronger than its previous close.
Government bonds were also a shade stronger, with the yield on the 2026 bond down 0.5 basis points at 8.49%.
Trump is due to give his address at lunchtime at the Economic Club of New York.
On the Johannesburg Stock Exchange, the All-share index was 0.6% higher.
Telkom SA shares were up 0.3% after the firm said half-year profit slumped by 36%. It had flagged to investors that profit could drop up to 40%.
(Reporting by Alexander Winning; editing by John Stonestreet)