The eight-month contract is for the upgrade of a 22km section of public road and the development of 13km of access road.
The project is expected to employ 80 people at its peak.
Based on permitting submissions, Atlas is planning to start mining at Corunna Downs next year.
Atlas is owned by Gina Rinehart's Hancock Prospecting.
"MACA is delighted to have been awarded these early civil works for Atlas demonstrating the civil capability within our end to end mining service offering," MACA CEO Mike Sutton said.
"We look forward to being part of the successful development of Corunna Downs and continuing our long-standing relationship with Atlas."
MACA has a long-standing working relationship with Atlas having previously provided services at the Pardoo, Mt Dove, Abydos and Wodgina operations, including being involved in a profit-sharing agreement with the company when the iron ore price slumped in 2015.
MACA is currently providing crushing services for Atlas' Mount Webber operations.
Separately, MACA also received notice of a 12-month extension to its Eastern Ridge mobile crushing contract for BHP until April 2021.
Shares in MACA were up 0.7% to 72.5c after hitting a 52-week low of 63.5c on Friday.
