South Africa head into their final qualifying game needing all three points, and for Benin to lose to Nigeria in their qualifier.
Cupido, who has six Bafana caps, was part of Broos' initial squad but failed to make the final cut ahead of Friday's goalless draw with Zimbabwe.
He has now been called up, to potentially replace Lyle Foster, who was inactive for part of Bafana's training on Monday.
A statement from Stellies read: "Stellenbosch FC striker Ashley Cupido has received a late call-up to the South Africa squad ahead of Tuesday's qualifier against Rwanda after being selected as an injury replacement by coach Hugo Broos.
"Cupido returns to the camp for the first time since 10 June 2025, when he last featured and scored his maiden goal for Bafana Bafana in a 2-0 friendly win over neighbouring Mozambique.
"In total, the 24-year-old has won six senior international caps to date and previously represented South Africa at the 2024 COSAFA Cup that was held on home soil in Gqeberha.
"He joins the squad at a time when Bafana Bafana currently occupy second position in the Group C standings and face a must-win encounter against Rwanda to secure automatic qualification to next year's World Cup.
"The match between South Africa and Rwanda is scheduled to kick off at 18h00 on Tuesday, 14 October, and will be played at Mbombela Stadium."