No, versioning is not possible in a file geodatabase. File geodatabases are designed to be edited by a single user and do not support geodatabase versioning. Versioning, a mechanism in which all data edits are recorded as rows in delta tables, is only supported in an enterprise geodatabase.
Enterprise geodatabases are referred to as ArcSDE geodatabases prior to ArcGIS 10.3. Beginning at 10.3, ArcSDE services and command line tools are deprecated. For more information on this, see the following links:
Where is the install for ArcSDE 10.3?
What's new in ArcGIS for Desktop 10.3: Geodata
To migrate data from a file geodatabase to an ArcSDE geodatabase, the Geodatabase Administration toolset contains tools for a variety of geodatabase management tasks. For more information, please refer to: An overview of the Geodatabase Administration toolset.