Yes. It is:
[[NSFileManager defaultManager] setAttributes:@{ NSFilePosixPermissions : @0666 } ofItemAtPath:(* insert filepath here) error:&error];
Docs
As in the POSIX standard, the app either must own the file or directory or must be running as superuser for attribute changes to take effect. The method attempts to make all changes specified in attributes and ignores any rejection of an attempted modification. If the last component of the path is a symbolic link it is traversed.
If your App don't own the file, the you have to elevate the privileges. You can change file permission only as ROOT. And the docs are clear about this:
Quote from Apple Doc
Note: Elevating privileges is not allowed in applications submitted to the Mac App Store (and is not possible in iOS).
[...] If you have to perform a task that requires elevated privileges,
you must be aware of the fact that running with elevated privileges
means that if there are any security vulnerabilities in your program,
an attacker can obtain elevated privileges as well, and would then be
able to perform any of the operations listed above.