Is there a way to search for Birth Certificates for an individual?
First, make sure that birth certificates exist in the time and place you're looking at.
In most of Europe, the answer to that question will be "no, not as such": most jurisdictions there used (or still use) vital registers as the primary record of events. These are bound books of forms that are filled out by hand by a registrar. Formats vary: you can find anything from one event per two pages to twenty or more events per side of a page. People could/can get extracts from the register, and those extracts are something like what you think of as a birth/marriage/death certificate, but they're not the primary record. The register-book is.
If the answer to the first question is "yes", then the next thing to find out is whether those certificates have been indexed anywhere: has anyone gone through and created an alphabetical listing, or typed the names into a computer-searchable file? If yes, then you can look through the alphabetical listing, or search the file. If the computer index is on FamilySearch, then you can search it using the "Records" option from the "Search" menu at the top of main-site FamilySearch pages.
Where and when are you researching? What records are available online depends on location and time period.
Thanks. Is there a general way to search for birth certificates?
It's not easy to give you instructions in a general way. Some locations captured certain information while others did not.
I do a lot of New York City research, so I'll tell you what I do researching there, knowing what info is generally included.
I restrict my search to the location by starting from the New York City Birth Collection at https://www.familysearch.org/search/collection/2240282 Then I format my search using the names of both parents. That can be useful for finding children I may not know about or children who were not named when the birth was registered. In this example, I know that Margaret's maiden is often misspelled, so I've left it blank.
And a good place to start, to know if births were registered in the time and place of your search, is the FamilySearch Wiki Vital Records page for the city/county/state/country.