Actually without iTunes, you can also transfer a file from Mac to iPhone. Try AirMore, this is a free App, and no need client in your Mac. Just a few steps for you:
1. Download and install "AirMore" in your iPhone;
2. Open "AirMore.net" in your Mac, and connect iPhone to Mac by scanning the QR code, it is wireless;
3. You will see the "Files" icon at the bottom of left bar, click it you will enter the "Files"interface, and there is a "Upload Files" button above, click it then you can choose the file you want to transfer from your Mac, and transfer it to your iPhone.
Quite easy, isn't it?
Airdrop is probably the easiest way for most files:
"AirDrop is Apple’s technology for sharing files across devices. You can use it to transfer files from one Mac to another, and also use it to transfer files from a Mac to an iOS device, or from one iOS device to another. On your Mac, choose Go > AirDrop in the Finder, and then, on your iOS device, make sure AirDrop is activated in the Control Center (swipe up from the bottom of the screen to access this setting). You can choose to allow transfers from Contacts Only or from Everyone; it’s best to choose the former.
Your iOS device needs to be awake for AirDrop to be active. On the Mac, drag a file onto the icon for your iOS device in the AirDrop window. On your iOS device, you’ll see a menu offering to open the file; this menu lists the apps that can open the file type.