Catalysis of the reaction: arachidonic acid + O2 + NADPH + H+ = 20-HETE + NADP+ + H2O. Arachidonic acid is also known as (5Z,8Z,11Z,14Z)-icosatetraenoic acid, and 20-HETE is also known as (5Z,8Z,11Z,14Z)-20-hydroxyicosa-5,8,11,14-tetraenoic acid.