Many other NFL players, coaches and owners around the league chose to show a sign of unity on the field before their games by linking arms and kneeling on the sidelines during the song. The display follows comments made by President Donald Trump Friday in Alabama.
President Trump spoke about the NFL at a rally, saying that NFL owners should fire players who choose to protest during the national anthem.
Wolfe explained why he stands during the anthem with a statement to ESPN.
"I stand because I respect the men who died in real so I have the freedom to battle on the field," Wolfe told ESPN. "Paying tribute to the men and women is why I stand. But everyone these days likes to find a reason to protest and that's their right."
"It's America and you are free to speak your mind. I just feel it's disrespectful to the ones who sacrificed their lives and it's maybe the wrong platform. But like I said to each their own it's AMERICA! The greatest country in the world and you reside here, then why do you stay. A lot worse places in the world to call home. Proud to be an American.
Wolfe, 27, was a second round pick by the Broncos in the 2012 NFL Draft.
Wolfe's teammate Shane Ray explained why he kneels with a series of Twitter posts on Saturday.
"...my grandfather was in the military," Ray tweeted. "Served in the army Ww2. If he could see how the president of the country he fought for treated his people and people of color he would stand with his fist high or take a knee right along with the others fighting for a voice."
"The heart of America is our military," Ray said. "There are multicultural people fighting together for us beyond what we see here at home."
"Those same people will come home and be discriminated against regardless of there military sacrifice. Simply because of the color of their skin."
"When I hear the anthem it's not the words that make me feel like an American. It's us as people for one moment feeling united standing together. It doesn't take a rocket scientist to realize we are kneeling because we need everyone's focus and eyes so that we can work for a change. We have your attention now. Time to start opening your eyes so that we can change and have all people proudly stand for our country."
Broncos president and CEO Joe Ellis issued a statement on Saturday night.
"Our players have shown a tremendous commitment to raising awareness for important societal issues by using their platform in a positive way," Ellis said in the statement.
"In addition to their hard work off the field, we have great admiration for their dedication to making our team the absolute best it can be. They've made incredible sacrifices to reach this level, and we recognize they give their all to our team and fans each and every day.
"As an organization, we could not be more proud, appreciative and grateful for our players. We'll continue to support them and work together to advocate for values of respect, diversity and inclusion."
The Broncos trailed the Bills 23-16 in the fourth quarter Sunday at New Era Field in Buffalo.