Cryptocurrency exchange platform FTX is trying to level up in the U.S. with more established competitors through a new ad campaign featuring the married couple of football great Tom Brady and model and businesswoman Gisele Bündchen.

The U.S. affiliate of international crypto derivatives exchange FTX plans to invest $20 million in the campaign, which begins Thursday during the National Football League season kickoff game between Tampa Bay and Dallas. The campaign will run during NFL broadcasts throughout October along with digital advertising components, the company said.

“We’re the newcomers to the scene,” said FTX.US President Brett Harrison, referring to the crypto services landscape in the U.S.

The company needs to familiarize consumers with its technology, customer service and offerings, while competing with incumbents like Coinbase Global Inc. or Kraken, Mr. Harrison said. “We know that we had to embark on some kind of mass branding, advertising, sponsorship type work in order to be able to do that,” he said.

That has led FTX into sports marketing.

Mr. Brady and Ms. Bündchen, who in an ad titled “FTX. You In?” call acquaintances including New York Jets superfan Fireman Ed to join the platform, in June said they would be taking an equity stake in FTX. The company said Tuesday that National Basketball Association player Steph Curry would receive an equity stake in FTX as well for serving as a brand ambassador.

FTX also forged a naming rights deal worth $135 million for the stadium where the NBA’s Miami Heat play, now called FTX Arena. And the company this year said it had reached a deal to become the official cryptocurrency exchange of Major League Baseball. Umpires will wear FTX logos on their uniforms as part of that agreement.

The high-profile partners help signal that FTX is a reliable and trustworthy company, Mr. Harrison said.

With rising interest in cryptocurrency, scams have followed. The U.S. Federal Trade Commission said reports of investment scams have skyrocketed since October 2020, with nearly 7,000 people between October and March reporting losses.

Mr. Harrison said the FTX campaign is trying to reach both those who are well-versed in cryptocurrency and have a number of options they can choose from, and those who are new to the space and don’t know where to start. He said the campaign is meant to drive general brand awareness along with new sign-ups, deposits, trades, app downloads and other activity. FTX worked with its creative advertising agency, dentsuMB, on the campaign, along with dentsu’s 360i on media efforts.

The cryptocurrency space has drawn strong interest, but the advertising component has presented some gray areas, said Robb Fahrion, co-founder of Flying V Group, a digital marketing company that has worked with crypto clients.

TikTok in July barred users from promoting sponsored content about cryptocurrencies, for example, after already prohibiting ad placements for cryptocurrencies, crypto trading platforms and more. Google last month further loosened rules around crypto ads that meet some requirements after banning them in 2018.

Gemini Trust Co., the cryptocurrency exchange founded in 2014 by Cameron and Tyler Winklevoss, suggested in a 2019 ad campaign that it could protect investors in the evolving arena. Some players in the industry push for people to use the term “digital currency” over “cryptocurrency,” arguing that the “crypto” term sounds less reliable.

The sector’s relative newness and shifting rules pose questions when planning a marketing campaign related to crypto, Mr. Fahrion said.

“Obviously there’s interest, obviously there’s belief in the products, in the projects, in cryptocurrency in general, but there’s still a lot of things that have to get fleshed out from a compliance standpoint,” Mr. Fahrion said. “And then that rolls all the way down into marketing and advertising as well as to where, ‘What can and can’t we do?’”

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Write to Megan Graham at megan.graham@wsj.com