Carmen is the daughter of former motor racing driver Jose Miguel Jordá, who introduced her to the sport at an early age.

[4] Almost two months later, on March 8, 2010, it was announced that Jordá had signed with Andersen Racing full-time to drive in the Firestone Indy Lights Series for the 2010 season.

Former rally driver and head of the FIA's Women & Motor Sport Commission, Michèle Mouton, described her as a "marketing gimmick", citing "Simona de Silvestro, Danica Patrick, Susie Wolff or even Beitske Visser" as better choices.

[14] Writing for Vice, James Newbold commented that the signing of Jorda had been "the wrong message", suggesting she got the position based on her looks rather than her performances in GP3, where she finished 29th in 2014, while only the series winner Alex Lynn also secured a spot with a Formula One team for 2015.

[15] In an interview with Motorsport.com, Jordá spoke of her surprise at Mouton's comments and her ambition to invite her to an F1 race so "she can better understand exactly what her plans are with Lotus".

In an interview with Motorsport.com he spoke of his hopes to unearth more female talent in the future, arguing that a lack of other women racing at a comparable level makes criticism of Jordá unfair.

[21] In early 2016, former Lotus test driver Marco Sørensen claimed that she had been as much as twelve seconds off his pace in simulator runs.

[22] This claim was rejected by Jordá, who told Spanish newspaper AS that her simulator times had been "more or less within a second" of fellow Lotus driver Romain Grosjean.

Speaking to Autosport magazine, then-current Indianapolis 500 driver and race-winning Indy Lights driver Pippa Mann commented that "it is extremely disappointing to learn that a racer with no notable results in any of the categories in which she has competed, and who believes and is quoted as saying that she does not believe we as female racers can compete, has been appointed to the FIA Women in Motorsport Commission.