Following an extended shakedown cruise to Brazil and post shakedown availability, Rhind steamed south again and from 5 July to 19 December 1940 conducted exercises in the Caribbean and patrolled off Martinique. Employed as carrier escort and engaged in fleet exercises during the first half of 1941, she joined Task Force 1 in June and through the summer steamed in the North Atlantic shipping lanes on Neutrality Patrol. In August she escorted Augusta, with President Roosevelt embarked, to Newfoundland for the Atlantic Charter conferences. Then, at their conclusion, she escorted HMS Prince of Wales, carrying Prime Minister Churchill, to Iceland. On 17 August she returned to patrol duty off the Newfoundland coast.

Detached in October, Rhind escorted Yorktown from midocean to Halifax in early November, then joined a Halifax-Capetown convoy as escort. Off Southwest Africa 27 November, she was detailed to escort Ranger to Trinidad. They arrived 3 December. Four days later the United States entered World War II.

Rhind then steamed north to patrol the waters off Bermuda. In February 1942, she shifted further north and through March escorted Icelandic convoys. In April she shepherded a convoy to the Canal Zone and on the 23d, while en route back to New York, conducted her first depth charge attack on a German submarine. (continued)