You could no doubt weld that with a nickle rod such as the Sodel 35... but I can just about promise you that the cost of the rod will exceed the value of that vice by the time you're done.
Honestly, simply for the value of the vice I'd toss it in the scrap bin and be done of it.
If you're just wanting to play with it to say you fixed it... and do it cheap... I think I'd braze it. 10 bucks worth of brazing rod will probably do the trick. I'd bevel it out a fair bit but not all the way through... just so you have enough original surface left to keep it straight... then clamp it and fill the gap.