In my last session with the game I'm running, one of my players wanted to grab an anchor that was nearby as a weapon. I know that I should treat it as a improvised weapon but since it's an anchor I was wondering what damage die should I use for it and since it is a big weapon, if I should impose disadvantage on all attack roll on it or not.
Change the description of a normal attack
The improvised weapon rules can slow the game and are often less effective than a PC's normal attack, which can discourage players from trying cool things. If a player wants to damage opponents in a novel way, it's easiest to mechanically conduct it as the PC's normal attack, but describe it as desired.
Story time: my half-orc barbarian player wanted to clobber the Big-Bad, using a nearby minion as a club (as you do), so I said "Sure. You normally have two attacks, so we'll assign one to each". He hit with both and we described the glorious carnage exactly as he specified. Of course: if he had only one attack, we would've still described it mostly the same (but only one opponent would've had their HP reduced).
Using this method, players really don't even need DM permission to describe their attacks in a cool way, since they are just following the normal rules. Plus, if the DM likes it: she is free to give Advantage or award Inspiration.
that totally depend on the anchor. I have seen small weight-anchors for dhingis that are basically a stick with a lead bulb on one end, an eye (for the rope) on the other end - this is more or less a heavy mace. Other anchors were of the two or three-pronged kind, and even without a chain attached, these handle about as well as any unbalanced klunky 5-50kg (yup, not for the faint at STR) steel contraption. They are all hard corners and edges, though, so if you manage to hit someone with it, it will do damage.
I'd raise the possibility of a fumble, and let it deal damage like a same-size mace while encumbering the wielder.