I am currently setting up my own SCCM 2012 lab environment. I have managed to get the SCCM primary site server and domain controller server that host AD, DHCP and DNS up and running and now i want to setup the DP role on the domain controller server.

I know that in a domain controller server doesn't have the local users and groups function. My question is how can I add the primary site computer account in the local administrators group in the DC server before i can proceed to add the DP role in my domain controller server?

Add the account to the Domain Administrators group (which is the "equivalent"). 

ConfigMgr is already running as local system on that system and does not need anything additional to install additional site roles; however, I would strongly advise you to remove ConfigMgr from your DC. Even if this is a lab, you should still try to do things similar to how they are done in the real world and in the real world installing ConfigMgr or any roles on a DC adds complexity, weakens security, and is highly discouraged. Installing anything on a DC is highly discouraged. Set up a second virtual machine and install it there.

But if You still want to add DP on domain controller then better add the account to Builtin\Administrators group, it has less privileges than Domain Admins

But if You still want to add DP on domain controller then better add the account to Builtin\Administrators group, it has less privileges than Domain Admins

As mentioned though, there's no need to as in this case, the site server is already running as local System and so can do anything that it wants to to the DC.

Why do You think ConfigMgr is running on DC? It is not mentioned that there is ConfigMgr client on DC.

Your case https://social.technet.microsoft.com/Forums/en-US/1a07fd37-94e4-4085-b3f6-610c7dd53896/sccm-2012-distribution-points-on-domain-controllers?forum=configmanagerdeployment

If you are using the DC as a Distribution point to install clients via Client Push, the "NT Authority\Authenticated Users" group must be added to the local group "Users" to the DC/DP.

Clients are still able to get installed manually, but Client Push fails.

Failed to correctly receive a WEBDAV HTTP request.. (StatusCode at WinHttpQueryHeaders: 401)

Run elevated command prompt (net localgroup users "Authenticated Users" /add)

Test Client Push - Should be successful.

Reason: By default the local groups NT Authority\Interactive Users and NT Authority\Authenticated Users are removed from the Domain Controller. Clients that are using the DP for content cannot authenticate using the computer account.

It just reads that way to me. I could be wrong though -- being specific and giving details when asking questions helps folks answer them.