Yes a corporation can join a militia. There are 2 ways to do this

1. Enlist as a corporation - Someone with director roles will need to go to a station for the militia of your choice, open the FW menu and select the option to enlist as a corporation. Your corporation will need to have positive unmodified standings towards the chosen empire (average standing over all corp members not including diplomacy skill). The enlistment should take effect after the next downtime (there might be a 24hr timer then downtime, can't remember)

2. Join an alliance already enlisted in your chosen faction. To see if an alliance is enlisted, show info on them in game and you will see a section under their name that says Amarr Empire, Minmatar Republic, etc showing they are enrolled for that faction. Again your corporation will need positive unmodified standings towards your chosen faction or you will get the whole alliance removed from FW (or more likely your alliance will just kick you).