Can I make someone turn around in Minecraft using Command Blocks?

Yep, it's fairly easy to do too. This is probably the command you are wanting:

/tp @p ~ ~ ~ ~ ~180

The syntax is: X coord, Y coord, Z coord, Y rot (up and down), X rot (side to side). "~" means relative, so the player stays at the same coordinates, and turns around 180 degrees.

However this was only added as of snapshot 14w03a, which is after the 1.7 updates that most servers and players will be on at the moment. As an alternative, you may want to have them press a button behind them each time they score a point; I don't know how your range works so can't really detail that.

There is indeed a way to do this with the new command blocks as mentioned by MBraedly. SethBling did a very nice cover of all the new command block neatness in one of his snapshot previews and shows one that makes you spin around. Find the video here:

The new features to the tp command are what you are after, about 4:30 in the video and it is as @MBraedley mentioned, adding in the heading and pitch values to it.

/tp @p ~ ~ ~ [heading]

The ~ are XYZ shorthand for where you currently are, for heading values use the ones displayed in the F3 overlay text. And I think that will take care of your needs.