From the Ant-Man movie ("we got guys who climb up walls") and interviews with Kevin Feige and the Russo brothers, it's already known that the Tom Holland Spider-Man will be established in the MCU (no more origin stories).
Now the website Geek.com is possibly providing further details.
According to a source in the know, Peter Parker decides to fight crime as Spider-Man because he is a big fan and idolizes Tony Stark/ Iron Man. It's said Captain America: Civil War takes place ten years or so after the first Iron Man movie, so Peter would have been 5 years old when he first saw the news broadcasts about Iron Man.
It's further said Tony Stark has been keeping tabs on "a certain young genius and his superhuman abilities" and goes to Peter Parker to recruit him with an offer of an "advanced Spider-suit to fight in," which is an upgrade from whatever the 15-year-old Peter Parker has been wearing. Obviously as Peter is such a big fan, he is completely in awe of Tony Stark showing up at his door and accepts the offer.
We can even speculate that further evidence to support the theory/rumor comes from the viral marketing surrounding Ant-Man as the [fictional] WHiH news reports mentioned Tony Stark setting up scholarships for "promising students" in urban schools (i.e. Peter Parker).
"Captain America: Civil War" has a May 6, 2016 release date directed by Anthony and Joe Russo starring Chris Evans, Robert Downey Jr., Scarlett Johansson, Jeremy Renner, Elizabeth Olsen, Sebastian Stan, Anthony Mackie, Frank Grillo, Paul Bettany, Don Cheadle, Emily VanCamp, William Hurt, Martin Freeman and Chadwick Boseman as Black Panther.
Captain America: Civil War picks up where Avengers: Age of Ultron left off, as Steve Rogers leads the new team of Avengers in their continued efforts to safeguard humanity. After another international incident involving the Avengers results in collateral damage, political pressure mounts to install a system of accountability and a governing body to determine when to enlist the services of the team. The new status quo fractures the Avengers while they try to protect the world from a new and nefarious villain.