Batsman

Full definition of batsman

(plural batsmen)

(cricket) A player of the batting side now on the field
(cricket) The player now receiving strike; the striker2001: The batsman, Kathryn Leng, (who has played for quite a few years for England) asked the umpire dumbfounded if Charlie was going to bowl with a helmet on. — Julia Price (Australian cricketer), her women's Ashes diary entry for 19 June 2001 http://www.southernstars.org.au/ukdiary2001.htm
(cricket) Any player selected for his or her team principally to bat, as opposed to a bowler

The term batsman is applied to both male and female cricketers; batswoman is much rarer.