How can I become a DevOps Engineer?
DevOps is not a role and in words of @Tensibai here:


  DevOps is roughly an organization pattern aiming at breaking the silo between developers and sysadmins.


So, you could already be on the DevOps moto and if you don't think you are, you can probably just try to implement the DevOps pattern on your organization or move to another organization with that pattern already implemented.

You may want to become an Infrastructure Engineer, a SysAdmin Engineer, an Automation Engineer, a Site Reliability Engineer, a Performance Engineer... but surely you can not become a DevOps Engineer.

You can get a good sense of your path by reading some questions and answers on this site. Here are a few ones:

What is DevOps?

What is the difference between DevOps engineer Vs DevOps consultant Vs DevOps architect?

What is the difference between SRE and DevOps?

What could be a valid definition of DevOps to introduce it to a novice?

What is the difference between the traditional Development and Operations 
Model and Site Reliability Engineering?

What is the difference between Sysadmin and DevOps Engineer?