Aribo scored in the 68th minute to put Rangers 2-1 ahead.
Other scorers for Rangers are Scott Arfield who got two goals and Alfredo Morelos.
Lewis Smith equalised for Hamilton Academicals in the first half.
And reacting to the win, Aribo praised his teammates for their performance describing it as solid.
He also hailed Rangers fans for their contribution to the win.
“In the hat for the next round, solid team display this afternoon! Always a good feeling to score. Thanks to all the travelling supporters,” Aribo wrote on his verified Twitter handle.
Rangers will know their quarter-final opponent in the Scottish Cup when the draw is decided today (Sunday).