Copying one video from Mac to Iphone without syncing
You can use iTunes to move files directly without a sync over USB.


Attach your iPhone, iPod or iPad with the datacable to your the Mac.
In iTunes, in the top right corner, click on your device. In my case it's an iPad.


Now go the the 'Apps' tab and scroll down to 'File Sharing'


Choose the program you want to sent your file to


Click on the 'Add' bottom in the bottom right




The newer versions of Dropbox app supports syncing from their servers and local WiFi syncing over a LAN so you can experiment with this if you don't want to try iTunes. Apple's documentation can be found here. There are also third party tools that sync files, but for one file it's hard to justify downloading anything and just use iTunes for the task.