Question

How did the war affect the migration of workers in the United States?

Answer 1

Assuming you're referring to WWII, one way in which the war affected the migration of workers in the United States was that it led to more immigration to the cities, since this was where many of the factories that were helping the war effort existed. 

Answer 2

Because it was not specified which War, lets talk about WWI and WWII:

WWI: The closing off of foreign immigration and the movement of 4 million men from the workforce into the armed services created an acute labor shortage across the wartime United States. To meet it, women, African Americans, and other ethnic minorities were encouraged to enter industries and take on jobs heretofore dominated by white men. Over four hundred thousand southern blacks (and a significant number of whites) began a Great Migration northward during the war years, a mass movement that continued unabated through the 1920s and changed the political and social dynamics of northern cities.

WWII:  Nearly 8 million people moved into the states west of the Mississippi River between 1940 and 1950. Lured by news of job openings and higher wages, African Americans from Texas, Oklahoma, Arkansas, and Louisiana headed west. The South also experienced dramatic social changes as a result of the war effort. Sixty of the one hundred new army camps created during the war were in southern states. The construction of military bases and the influx of new personnel transformed the local economies. Manufacturing jobs led tens of thousands of “dirt poor” sharecroppers and tenant farmers, many of them African Americans, to leave the land and gain a steady wage working in mills and factories. Throughout the United States during the Second World War, the rural population decreased by 20 percent.