For most of the counties in Texas, searching for arrest record and warrant information can be extraordinarily difficult. This is because, for most of the state, individual websites do not exist for the sheriffs of those counties. This is not the case for Fort Bend County, Texas.
By visiting the home page of the Fort Bend County Sheriffs Office at http://www.co.fort-bend.tx.us/getsitepage.asp?sitepage=3219, you will be granted access to a great deal of the various official records provided by the state. Although we cannot list those records themselves on this page, we can direct you to different parts of this website which will be useful to you.
Although this website does not seem to provide a list of current arrest warrants for Fort Bend County, they do have a page that details how they function within the county. You can either visit this page at http://www.co.fort-bend.tx.us/getSitePage.asp?sitePage=39564, or call their warrant division at 281-341-4534.
You can look at the Most Wanted alleged criminals in the county at this page: http://www.co.fort-bend.tx.us/getSitePage.asp?sitePage=5520. You can also look at criminal statistics for Fort Bend County, Texas at this page: http://www.co.fort-bend.tx.us/getSitePage.asp?sitePage=20467. It details all of the information with the visual convenience of a map.
Resources which you may find useful that are not provided by this county but rather by statewide institutions include the Offender Information Search at https://offender.tdcj.texas.gov/OffenderSearch/index.jsp , and the Criminal History Name Search at https://records.txdps.state.tx.us/DpsWebsite/CriminalHistory/.