Alec Baldwin's trial for the fatal shooting on the "Rust" movie set begins Tuesday ... and cops are beefing up security out of precaution, TMZ has learned.

Denise Womack-Avila, spokeswoman for the Santa Fe County Sheriff’s Office, tells TMZ ... due to the actor being so high-profile, and the amount of media interest in the case, additional deputies will be working the courthouse and the surrounding area to maintain peace and safety.

She did not go into specifics about what that might look like as far as numbers -- that's a typical precaution for law enforcement, so as not to tip its hand to the media ... but it's clear AB's presence raises the stakes.

Alec's had plenty of contentious interactions with photographers and ordinary citizens attempting to troll him -- so, crowd control outside the courthouse, as he enters each day, will be critical.

Womack-Avila also told us media and normies looking to get a spot in the courtroom are not allowed to camp out at the courthouse. They have to follow the daily protocol to be admitted in the morning.

As TMZ previously reported, Alec is already in Santa Fe ... the actor was present Monday for a pretrial hearing, sporting a suit and tie with thick black glasses.

AB is charged with involuntary manslaughter in the shooting death of "Rust" cinematographer Halyna Hutchins in October 2021.

Alec has pled not guilty ... "Rust" armorer Hannah Gutierrez-Reed has already been convicted of manslaughter for her role in the incident ... though she is appealing her sentence.

The trial kicks off with jury selection -- but even before that, cops will be focused on security in and outside the courthouse.