The DS Techeetah FE driver is set to drive the Honda-powered Dallara at Barber Motorsports Park in Alabama on November 2.
Former BMW DTM driver Da Costa is known to team co-owner Bobby Rahal through long-standing connections with the German manufacturer.
The five-time E-Prix winner previously raced for the marque’s Andretti-run FE squad and FIA World Endurance Championship program, with da Costa developing the M8 GTE racer ahead of its competitive debut in the 2018 Rolex 24 at Daytona.
Rahal's team, meanwhile, runs the works BMW squad in the GT Le Mans category of the IMSA WeatherTech SportsCar Championship.
Da Costa said: “I have never hidden the fact that it’s a big dream of mine to come try out an IndyCar.
“I am a big fan of how America, and IndyCar in particular, goes about the sport and have been a huge fan for many years.
“I have known Bobby for a few years. We always met at the BMW Christmas dinners and every year I kept saying ‘Come on, let me have a go!’ and finally now I got the call to come meet the team and test.
“It’s very exciting times for me and something I have been looking forward to a lot. The first contact with the team has been very positive and everyone has been friendly.
“I can see there is a high level of professionalism in the team which was to be expected. I’m excited to get on track.”
Rahal, who co-owns the RLL IndyCar squad with renowned former talk show host David Letterman, added: “We were unable to maximize a full team test using one of our three days, since Graham is waiting the arrival of his first child so this enables us to test a young and very accomplished driver in Antonio Felix da Costa.
“Through our partnership with BMW on the sportscar side, we have followed his career and are excited to see what he can do in an IndyCar.”
Fellow team co-owner Mike Lanigan said: “We have heard a lot of great things about this young man’s talent and look forward to good results from our test at Barber Motorsports Park.
“It always adds value to get another perspective and we are confident he can provide good insight.”