In order to deploy a trigger from sandbox to production, you need to take care of some points:

• At first I would like to request you all that before going for any deployment, make sure that there is no test failure or less than 75% code coverage in Production Instance. Because when we deploy any thing from sandbox to Production, “Run All Test” is performed automatically in Production. If there is any issue in Production then it will not let you deploy your new code.
• If you are deploying any trigger in Production, then you must write a test class for that trigger with no Test failure and more than 75% code coverage.
• Create deployment connection in sandbox.
• Create Outbound change set in Sandbox and add your trigger and its associated test class in the change set.
• Create Inbound change set in Production.
• Add Change set components in Sandbox.
• Upload the change set.
• You can validate the change set in Production.
• Finally deploy the change set in Production.

Hope this will help to deploy a trigger from sandbox to production.