The word "budge" means to move slightly or make a slight movement. In the context of synonyms, there are many words that can be used instead of "budge". Some of the synonyms can be "shift", "stir", "move", "twitch", "adjust", "displace", "nudge", "shuffle", "swing", "transfer", "slide", "slip", "veer", "tilt", "tip" and "turn". These synonyms all imply movement, but they each have their own unique connotations and nuances. Depending on the context, one of these synonyms may be a better choice than another to accurately convey the meaning intended by the speaker or writer.