Despite having a fairly robust website, finding arrest warrant information for Galveston County, Texas wont be as easy as entering a few names into a search panel. This means, specifically, that you will need to contact the Galveston County Sheriffs Office yourself in order to request this kind of information.
You may call the warrant division of the Galveston County Sheriffs Office at 409-766-2311.
Thankfully, finding information that concerns arrest records for Galveston County is an easier and entirely-online process. There are two tools that we advise people use.
For getting a criminal history search for a particular person, you should use the Texas Department of Public Safetys search tool, which you can find here: https://records.txdps.state.tx.us/DpsWebsite/CriminalHistory/.
If you combine the results from the Texas DPS search with the results from the Texas Department of Criminal Justice, whose tool is found at https://offender.tdcj.texas.gov/OffenderSearch/index.jsp , you can put together a surprisingly detailed criminal history of the person that youre searching for.
Although there certainly are a number of services on the internet that will sell you access to this information, it can often be easier to just instead go through the official channels.