After emerging as one of the nation's top prep players at Penn High, she headed to Purdue University's women volleyball team, with which she took part in the NCAA Division I Championships from 2012 to 2015.

Drews was named the league's MVP after leading Caquas Criollas to a 16–0 start and the Puerto Rican title.

Her performance started catching the eye of Kiraly and SASB Volleyball Legano, the club in Italy's Serie A1 she eventually signed with.

In the 2017-18 championship she played in the Italian A1 Series in the newly promoted SAB Volley Legnano, ending her contract with the team in December 2017.

During the 2018-2019 pro season, she signed with Kameroglu Beylikdüzü Voleybol Ihtisas and played at the Turkish Volleyball League.

In 2019, Drews signed with JT Marvelous to play in the Japan V.League Division 1 (V1), replacing Serbia women's national volleyball team outside hitter Brankica Mihajlović.

[9] Due to prior commitments with the USA national team (participation in the 2019 Women's NORCECA Volleyball Continental Championship), she missed the season's first two games.

"The extra work paid off with a spot on the U.S. roster for the 2017 FIVB Volleyball World Grand Prix finals round.

Although the U.S. did not win either of its Finals Round matches against Serbia and Italy, Drews came off the bench in both contests to provide a huge spark.

Drews was the U.S.' top scorer (16 points: 15 kills in 39 swings for a 38.46% hitting efficiency; and 1 ace)[17] in a 3–1 loss to Italy.

Drews returned for duty as she joined the U.S. team for the 2017 FIVB Volleyball Women's World Grand Champions Cup.

[19] In 2018, Drews joined the U.S. team in the inaugural 2018 FIVB Volleyball Women's Nations League where they eventually won gold against Turkey (25-17, 22–25, 28–26, 15–25, 7–15).

Annie Drews led Team USA with 23 points, including 21 kills on 41 attacks, one block and one ace against Poland in the finals pool play.

[21] After the win, Kiraly did not spare kind words for the tournament MVP Andrea Drews after the match"Wow, Annie.

"On 2–4 August, Drews competed with USA in the 2019 FIVB Women's Volleyball Intercontinental Olympic Qualifications Tournament (IOQT) in CenturyLink Center, Shreveport-Bossier City, United States.

[22] Drews was lined-up for another round of NT duties at the 2019 FIVB Volleyball Women's World Cup in Japan from September 14–29.

[24] USA bagged another impressive straight sets victory against Brazil with Drews having 12 attacks on 27 swings (44.44% hitting efficiency) and 2 stuff blocks for 14 points.

[25] In their 3-set loss against eventual gold medalists China, Drews, used sparingly, contributed 6 kills on 12 swings (50% hitting efficiency).

[26] In their bounce-back win against Dominican Republic, Drews posted an impressive 23 points in 3 sets mounted from 18 attacks on 29 swings (62.07% hitting efficiency), 3 stuff blocks and 2 aces.

[27] USA gutted out a 5-set outing against Russia anchored on Drew's 20 attacks on 46 swings (43.48% hitting efficiency), 1 stuff block and 1 ace.

In their final match of the tournament vs. South Korea, Drews gave out an impressive 20 attacks on 41 swings (48.78% hitting efficiency), 2 stuff blocks and 2 aces for 24 points.

[29] South Korea women's national volleyball team head coach, Stefano Lavarini, gave praise to Drews' performance in the post-match interview saying:"We couldn't put pressure on their service and the United States in the first two sets, but especially the second, played really strong and their attackers were almost unstoppable, most especially their incredible opposite Andrew Drews.

For the final round of 2019 national team duty, Drews was lined-up for the 2019 Women's NORCECA Volleyball Continental Championship held in San Juan, Puerto Rico from 8–13 October.

USA eventually won the match in straight sets as she added eight kills on 14 swings and a block for nine points.

Drews started nine of the 11 World Cup matches and converted 45.3 percent of her attacks into points with a .324 hitting efficiency.

[33] In May 2021, she was named to the 18-player roster for the 2021 FIVB Volleyball Women's Nations League tournament that was played in Rimini, Italy.

[34] Her debut match against Canada saw her scoring 20 points (19-4-37 att, 51.4% hitting efficiency; 1 ace) to lead the US in a straight-sets victory.

[38] USA capped their third round of VNL action beating Italy, three sets to one, led by Drews' 20 points (18-3-30 att, 60% hitting efficiency; 2 aces).

[40] Drews was initially slotted as for an off-the-bench role but assumed starting opposite duties when Jordan Thompson went down with an ankle injury.

After landing at the top of their pool, the United States went unbeaten in the medal rounds, winning all their matches without dropping a single set.