Angerer was born in Lohr am Main, near Frankfurt. Her career began with ASV Hofstetten, where she played as a forward. When she substituted for the injured goalkeeper during a youth scouting game, she was discovered as a goalkeeping talent. In 1995, she moved to 1. FC Nürnberg and one year later to FC Wacker München. While at Wacker, she rejected the opportunity to play for an American college soccer team.

Angerer made her international debut for Germany against the Netherlands in August 1996. However, after five matches in quick succession she was only used sporadically thereafter. Angerer was Germany’s second choice goalkeeper behind Silke Rottenberg for almost a decade, winning six major titles as a reserve player without having played in a single game, including the 2003 FIFA Women’s World Cup, two Olympic bronze medals in 2000, 2004, and three UEFA European Championships in 1997, 2001 and 2005.

From 1999 to 2001, Angerer played at FC Bayern Munich, helping the team achieve promotion to Germany’s top division, the Bundesliga. She transferred to 1. FFC Turbine Potsdam in 2001, where she claimed two national Bundesliga championships, three German Cup wins and the UEFA Women’s Cup in the 2004–05 season.

After seven years at Potsdam, Angerer left Germany in 2008 to play at Djurgårdens IF Dam in Sweden, replacing Bente Nordby. She returned to Germany after only one season to join 1. FFC Frankfurt. She won the German Cup for a fourth time with Frankfurt in 2011. Following Birgit Prinz’s retirement she was appointed Frankfurt’s new captain.

Angerer remained Germany’s national team goalkeeper for the 2008 Summer Olympics, claiming the bronze medal. She won the European Championship for a fourth time in 2009, the first time she had been a starter for Germany. Angerer was called up for the 2011 FIFA Women’s World Cup squad and received her 100th cap in her team’s second match of the tournament, against Nigeria.

After abandoning an apprenticeship as an event technician, Angerer trained as a physiotherapist and took a break from the national team in 2006–07 to complete her exams. Angerer told the German newspaper Die Zeit in December 2010 that she does not discriminate on grounds of gender when considering personal relationships.

Following Birgit Prinz’s retirement Angerer was appointed the national team’s new captain. She saved penalty kicks from both Trine Rønning and Solveig Gulbrandsen during the UEFA Women’s Euro 2013 final at Friends Arena on 28 July 2013, and was named player of the match following Germany’s 1–0 win against Norway. Anja Mittag’s goal gave the Germans their sixth successive title.

On 13 January 2014, Portland Thorns FC announced Angerer’s acquisition to play for Portland for the National Women’s Soccer League 2014 Season, replacing Karina LeBlanc who was traded to the Chicago Red Stars. She made her debut for Portland with a shutout against the Houston Dash on 12 April and went on to start 22 games for the Thorns, adding another three saves while compiling 74 saves (both ranking fourth in the league). After the season, Angerer was loaned to the Brisbane Roar with plans to return to Portland for the start of the 2015 season.

Angerer retired from being a professional footballer in 2015.

In May 2015, Angerer was named to Germany’s roster for the 2015 FIFA Women’s World Cup in Canada. During a quarter-final match against France, she denied Claire Lavogez who took the crucial fifth penalty during the penalty shootout to clinch the win and advance to the semi-finals against the United States. Germany lost the semi-final 2–0 to the United States after Carli Lloyd scored a penalty and Kelley O’Hara added a second goal. In Angerer’s final game with the national team she was beaten by another penalty, despite her angry protests. Fara Williams gave England a 1–0 extra time win in the bronze medal match.

On 2 December 2015, Angerer was announced as the goalkeeper coach for the Portland Thorns.

Angerer married her long time girlfriend Magdalena (née Golombek) in November 2016.

On July 17, 2020, Angerer was signed as an emergency replacement goalkeeper by Portland Thorns FC during the 2020 NWSL Challenge Cup.