Permission to create linked server
There is no requirement for sysadmin to create a SQL Server Linked Server .

Assigning  the permissions ,ALTER ANY LINKED SERVER and ALTER ANY LOGIN to a login account  , allows the actions to complete.


  Create a Linked Server with master.dbo.sp_addlinkedserver.
  
  ALTER ANY LINKED SERVER permissions are required


Drop a Linked Server with master.dbo.sp_dropserver.
ALTER ANY LINKED SERVER permissions are required

Create the mapping of a local login with a remote server with master.dbo.sp_addlinkedsrvlogin

Code examples: Assigning permissions

USE master;
GRANT ALTER ANY LINKED SERVER TO MYLOGINACCT;
GO
USE master;
GRANT ALTER ANY LOGIN SERVER TO MYLOGINACCT; 

--An example of adding a Linked Server 
EXEC sp_addlinkedserver      
@server='Server1',    
@srvproduct='',   
@provider='SQLNCLI',    
@datasrc='Server1\instance1'

---An example of dropping a Linked Server 
EXEC master.dbo.sp_dropserver ‘Server1’


Link: http://www.sqlserver-dba.com/2011/05/sql-server-linked-servers-and-user-permissions.html