Global Quick Actions and Object Specific Quick Actions can be deployed via ANT tool in Salesforce.

Sample Package.xml:

<?xml version="1.0" encoding="UTF-8"?>
<Package xmlns="http://soap.sforce.com/2006/04/metadata">   
	<types>
		<!--Global Quick Action -->  
		<members>LogACall</members>
		<!--Object Specific Quick Action -->
		<members>Task.TestingAction</members>
		<name>QuickAction</name>
	</types>
	<version>36.0</version>
</Package>