The earliest non-chance way to get a corrosive weapon is to do the side mission "Rock, Paper, Genocide: Corrosive Weapons!" which becomes available from Marcus shortly after you get to Sanctuary. (You'll need to docomplete his fireincendiary and shock weapon missions first.) He'll give you a corrosive weapon (usuallyinvariably a pistol, I thinkit seems, but the type varies) in order to shoot the target dummy, which. At this point you can keep during that game session ifleave the mission be (do not shoot the target dummy!) and you avoid turning inwill have that mission. Howeverpistol from that point on, though the weapontype will no longer be therechange randomly if you loadreload from a save. (i.e., start a newIf you shoot the dummy you'll have the pistol for the rest of that game session), but it will not reappear if you reload from a save.)