Current line highlighting in TeXstudio
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.
For those of you who can´t find that setting under "Editor": See this little checkbox on the bottom left saying "Show Advanced Options"? Click it and go to the new point "Syntax Highlighting", scroll down to "Line highlighting" and here you go :)