No, it is still not part of the MCU
According to this article and Wikipedia, Tom Holland will be playing Spider-Man in the new movies, whereas Andrew Garfield played him in The Amazing Spider-Man.
Kevin Feige, president of Marvel Studios, has also made it very clear that this is a new version of Peter Parker:
In terms of the age of what we believe Peter Parker is, I’d say 15-16 is right…We want to play with Spider-Man in the high school years because
frankly there’ve been five Spider-Man films and the amazing thing
about it is, even though there’ve been five Spider-Man films, there
are so many things from the comics that haven’t been done yet.
Note that this contradicts The Amazing Spider-Man.
According to Feige:
I think it was midway through the first film that he graduated high
school. At the beginning of the second Marc Webb film, he graduated
high school. And some of my favorite Spider-Man arcs and Spider-Man
stories, he’s in high school for a lot of it.
The Marc Webb films are The Amazing Spider-Man and The Amazing Spider-Man 2.
Since Spider-Man will be in high school for Captain America: Civil War, it is clear that Feige is going for a very different story for Peter than happened in The Amazing Spider-Man.
Similarly, from an official Marvel article,
New Spider-Man Will Appear First in an Upcoming Marvel Film Within Marvel's Cinematic Universe
Under the deal, the new Spider-Man will first appear in a Marvel film
from Marvel's Cinematic Universe (MCU). Sony Pictures will thereafter
release the next installment of its $4 billion Spider-Man franchise,
on July 28, 2017, in a film that will be co-produced by Kevin Feige
and his expert team at Marvel and Amy Pascal, who oversaw the
franchise launch for the studio 13 years ago. Together, they will
collaborate on a new creative direction for the web slinger. Sony
Pictures will continue to finance, distribute, own and have final
creative control of the Spider-Man films.
This constitutes explicit confirmation that the version of Spider-Man appearing in Civil War is an entirely new iteration of the character.