FIFA had made it clear the multi-coloured armband, introduced to support diversity and inclusion, was not welcome at the 2022 men's World Cup in Qatar.
As a result, a number of European nations abandoned plans to wear it after being warned they would face sporting sanctions, including their captains being booked or ordered to leave the pitch.
Williamson said England are determined to continue showing their support after wearing the armband throughout their triumphant run to the Euro 2022 title.
"It's something we want to do all year round and we've done previously," Williamson told a news conference ahead of their opening match at the Arnold Clark Cup against South Korea on Thursday.
"The statement that was made at the Euros with every team participating was incredible, every picture we have with a trophy lift there's a rainbow armband in there.
"It's a great stage and a great time to promote the values we believe in so much, so I hope it's the same."
Williamson added England would never stop standing up for what they believe in.
"We're a squad that promotes inclusivity and equality, we obviously have a number of people that feel very strongly about it," she said. "It's not even a question for us."
The England captain also referred to the Czech Republic international Jakub Jankto (27) who on Monday announced that he is gay, saying he wants to live his life "in freedom".
"You've seen another men's player step out and be as brave as they can be and they've changed their whole life. They don't know what's coming," she added.
"So, for us to stand in solidarity with that is important to us but it's something we've always done, it's something we'll continue to do.
"We're not just impacting football, we're trying to have a positive impact on society too and that's one of the ways we can do that."
The 2023 World Cup, played in Australia and New Zealand, will start on July 20.
