Sources within the Capitol Police tell TMZ ... cops were anticipating the landmark SCOTUS decision and they've been bracing for protests and preparing their response, beefing up security at the Capitol to address any civil unrest.

The Supreme Court does have its own police force, but we're told CPD is currently at the Court to bolster the ranks there, in addition to patrolling the Capitol.

All Capitol Police officers are now working extended duty -- we're told what is typically an 8-hour daily shift is being boosted to 12 to 16 hours on duty.

Tensions are high after SCOTUS overturned the 50-year-old precedent that legalized abortion nationwide ... and we're told the protests forming outside the Capitol feature both pro-life supporters and pro-choice advocates.

The way Capitol Police sees it ... anytime there are crowds of people on opposing sides, it's a recipe for potential violence.

We're told officers are just monitoring the crowds for now ... but it's clear they are prepared for the worst, some are already suited up in riot gear.

In another sign of the times ... we're told in addition to a security fence around the Supreme Court, there are snipers positioned on the roof of the building.

The Supreme Court's own police force is small, which is why Capitol Police are sending over more manpower.