Rosendahl was born in Chicago, Illinois, although his family subsequently relocated to Kansas and Texas and, in 1910, he was appointed to the Naval Academy from the latter state and was later commissioned in the rank of ensign in June 1914, upon graduation from the Academy, he was ordered to join the armored cruiser off Mexico during the Veracruz crisis. After "West Virginia" was decommissioned he served briefly on the battleship and the protected cruiser , before reporting for duty aboard the protected cruiser on May 14, 1915. On September 15, 1916 he returned to the recommissioned "West Virginia", which was subsequently renamed the "Huntington". On June 19, 1917 he received promotion to lieutenant (j.g), and to full lieutenant on August 31, 1918, having served aboard the "Huntington" escorting convoys of troops and supplies to Europe during World War I.