Yes there is a source with the State of Oklahoma for online birth records. However, it is not the actual record but an index of the birth records at a county level. It is a good start but is not perfect as it can have more errors than one would like. Records before 1950 can be based on delayed birth records (which is not indicated) which means a person (and some did) could claim what ever they wanted for a birth date and location. Any record found with a birth date prior to statehood in Nov 1907 is 100% a known delayed birth record and it not uncommon for someone to claim not where they were actually born but the first place they remember growing up. Then there is the problem with input errors for the index that sadly are also common with errors on spellings and dates.
Getting a copy of the actual record is also not as easy, for good reasons, any more as it once was. You also have may have to search more than one way to find a record. For some reason even when the info you enter is a an exact match it does not find what is on the index and never assume you know the correct name first name spelling or when you do know the correct spelling do not assume it will be correct on the Index.
Also remember that there was a time when people could file for a delayed birth record in one state claiming their birth was in a different state. For example I have found delayed birth records completed in Texas claiming birth in Oklahoma.
So with the above warnings below is the link
You can determine this by doing a search of the Historical Records section and looking through the Collection Listing for Oklahoma
Keep in mind that even if the answer to your question is technically "no"
You still could very well find a birth date - on a non birth record (an obituary, a church record etc.)