The unemployed man, Ng Ah Chye, allegedly did so on three occasions between July 11 and August 17 last year.
Ng allegedly approached a 32-year-old Indonesian woman on July 11, between 8.30am and 9.30am while she was gaming at a baccarat table.
She allegedly agreed to wager private bets with him instead of the casino on three occasions.
She allegedly wagered between S$500 and S$2,000 each time.
A similar incident allegedly took place on August 7 last year.
Ng allegedly wagered private bets with a 63-year-old man who was a member of the Crockfords Club at RWS.
Ng faces three charges in total and will be back in court on April 19.
Anyone found guilty of the offence can be fined between S$20,000 and S$200,000 and jailed for up to five years.