Arge was a member of the Royal Danish Academy of Sciences and Letters; he was elected to the presidium of the academy in 2015,. and became secretary-general of the academy in 2016. In 2012, he was elected as a Fellow of the Association for Computing Machinery "for contributions to massive data algorithmics", becoming only the second ACM Fellow in Denmark.ACM Fellow award citation, retrieved 2015-06-10.. He also belonged to the .
