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8 year oldTeam-mate Eric Reid knelt with Kaepernick, while two others - Antoine Bethea and Eli Harold - raised fists during the Star Spangled Banner.
The game was broadcast nationally to a Monday Night Football audience.
The Rams' Kenny Britt and Robert Quinn also held their fists in the air.
Back-up quarterback Kaepernick has refused to stand for the national anthem to highlight what he says is oppression of black people in the United States.
His stance has divided opinion in America - Kaepernick's jersey is now the best-selling replica kit in the NFL, but opponents say he is disrespecting the American flag.
Several players joined his protest in the NFL's opening weekend - which also marked the anniversary of the 9/11 attacks on the World Trade Center.
Many raised fists or knelt to support Kaepernick.
Four Miami Dolphins players - Arian Foster, Jelani Jenkins, Michael Thomas, and Kenny Stills - knelt as the Star Spangled Banner played.
Their opponents, the Seattle Seahawks, locked arms as they stood.
Kansas City Chiefs players also locked arms to show unity, while Marcus Peters raised a black-gloved fist - a gesture reminiscent of US sprinters Tommie Smith and John Carlos as they stood on the podium following their 200m final at the 1968 Olympic Games in Mexico City.
In a statement, the Chiefs players said it was their goal to be "unified as a team and to be respectful of everyone's opinions" as well as remember 9/11.
It continued: "It's our job as professional athletes to make a positive impact on our communities and to be proactive when change is needed."
Dolphins linebacker Jenkins said: "I chose to get involved to see if I could create change, raise awareness.
"I want to make it clear that there is no disrespect to the military or to police officers. I'm not about that.
"I would like to keep moving forward in the right direction with everybody: equal rights, equal opportunity.
"It doesn't seem that it's happening. That's why I took a stand."
Seahawks players and staff had been in talks before their game to discuss how best to show support, and now want to meet law enforcement officials.
New England Patriots duo Martellus Bennett and Devin McCourty also held up their right arms, while team-mate Danny Amendola was seen to grab the unfurled American flag on the field during the anthem.
In Thursday's season-opener between the Denver Broncos and the Carolina Panthers - a repeat of last season's Super Bowl - Denver linebacker Brandon Marshall knelt during the national anthem.
James Cook, Los Angeles correspondent, BBC News
"As the Star Spangled Banner was played on a violin, tens of thousands fans stood in silence. The entire field was covered in a huge American flag and on the sidelines Colin Kaepernick and teammate Eric Reid knelt in protest.
"Some fans shouted at them to get up. They have been accused of disrespecting their flag and their nation but many other fans say they approve of the demonstration - which is aimed at highlighting inequality in the United States. The quarterback, who is African-American says too many black people are killed by police officers - and too many still do not have the same opportunities as white people.
"The protests, which began in pre-season games, have spread, with players from other teams raising their fists in the air during the anthem - recalling a controversial salute by two black American sprinters at the 1968 Olympics."
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