Unfortunately, while libarchive.dylib and libbz2.dylib are included in the iOS SDK, the header files are not. This means that they are private APIs and cannot be used if you intend to submit to the App Store.
Never fear! This repository contains everything you need to build a static version of libarchive for iOS. libbz2 is also included for extra goodness.
To keep naming of things sane, we build the library as libarc.a.
If you just want to get going for iOS 4.2+, grab the header files and library in the build-for-iOS-4.2-8C134 directory.
If you need to build this for a different version of iOS, you can easily modify the build.sh script to point to whatever SDKs you like. It should build fine on 3.x.
One last note: libarc.a links dynamically to libz.dylib -- this is okay since, for whatever reason, AAPL saw fit to include the libz headers in the iOS SDK.
The current libarchive version is 2.8.4. The bzlib2 version is 1.0.6.