Upvote:20
The sinking of the Reuben James contributed to the American war sentiment, and the U.S. and Germany went to war six weeks later. The sinking of the Lusitania in 1915 contributed to U.S. war sentiment, and America entered the war in early 1917, almost two years later. Both events were smoothed over (temporarily) when the Germans showed subsequent restraint.
But the trigger events for America's entry in both wars were existential threats. For World War II, it was the Japanese bombing of Pearl Harbor. In 1917,it was the Zimmerman Telegram proposing a German-Mexican alliance. Both were regarded as stabs in the back.
The sinkings of the Lusitania and Reuben James did not rise to the above levels.
Upvote:24
why didn't America join the war after it sank?
Because, according to the Constitution (Article 1 Section 8), war is declared by Congress, and Congress was heavily isolationist.
Also, for all practical purposes, US was already at war:
When Hitler declared war on the US, he mentioned that "they are already fighting us anyway".
As an extended reply to a comment
why didn't the President declare military action, based on the attack of one of their ships, (forcing Congress to go to war, because they would have no other choice once we actively attacked Germany)
FDR could not afford to give more ammo to the isolationists, who already were outraged by the aforementioned actions. His political opponents were many and varied - from Nazis and Communists (although the latter switched sides on 1941-06-22) to traditionalists who love to mention Washington/Jefferson's "entangling alliances".
The even more important issue were the people. FDR understood that the war will be a hard fought all-out effort. He had to make sure that the people will keep morale high and not think "we provoked the war ourselves, it's our own fault, let's settle".
Seriously, what could FDR do that he was not already doing? Building a battleship takes 2-3 years. Making 1000 strategic bombers takes similar time. Mobilization, training the troops, arming them takes time.
US was in no position to do anything it was not already doing.
See also the Details section in another answer.