The tie will be played on Sunday 16 April, with a place in the final at Wembley Stadium up for grabs.
United advanced to the penultimate round of the competition for the first time on Sunday, following a 3-1 victory at Lewes in the quarter-finals.
The last-four draw was made a short time ago, on BBC One's Morning Live show.
Albion were United's first-ever Women's FA Cup opponents back in the fourth round of the 2018/19 competition - a game we won 2-0 away from home - and are a side that Marc Skinner's team have already had success against this season, triumphing 4-0 against at Leigh Sports Village in October's WSL meeting.