Options --> Configure TeXstudio --> Syntax highlighting. In the list of all the highlighting options, scroll almost to the bottom, to the end of the Line highlighting part. There you will find current, where you can define the colouring for the current line. The middle colour is the background colour.

Old answer, which probably applied to an older version of TeXstudio
Options --> Configure TeXstudio --> Editor. In the list of all the highlighting options, scroll almost to the bottom, to the end of the Line highlighting part. There you will find current, which defines the background colour of the current line.
