Necessary Privileges for Creating Database Links

A database link is a pointer in the local database that lets you access objects on a remote database. To create a private database link, you must have been granted the proper privileges. The following table illustrates which privileges are required on which database for which type of link:

Privilege	Database	Required For
`CREATE DATABASE LINK`	Local	Creation of a private database link.
`CREATE PUBLIC DATABASE LINK`	Local	Creation of a public database link.
`CREATE SESSION`	Remote	Creation of any type of database link.

To see which privileges you currently have available, query ROLE_SYS_PRIVS. For example, you could create and execute the following privs.sql script (sample output included):

SELECT DISTINCT PRIVILEGE AS "Database Link Privileges"
FROM ROLE_SYS_PRIVS
WHERE PRIVILEGE IN ( 'CREATE SESSION','CREATE DATABASE LINK',
                     'CREATE PUBLIC DATABASE LINK')

or just execute following query to see all the permissions for current user:
SELECT DISTINCT PRIVILEGE AS "Database Link Privileges" FROM ROLE_SYS_PRIVS

Source: Oracle Docs