After another failed attempt at stealing a sheep from Sam Sheepdog, Ralph Wolf returns home after his shift to relax and enjoy some television in his chair. Daffy Duck bursts in and declares that Ralph is the newest contestant on the game show "Sheep, Dog, and Wolf" or as Daffy likes to call it, "Who Wants to Be a Sheep Stealer". Daffy drives Ralph to Acme Town where the game will take place, telling him not to screw up as his performance reflects on Daffy. During a training session, Daffy explains the rules of the game which are that Ralph will be provided with numerous Acme products that can be used to formulate a plan to steal Sam's sheep who must be placed in a designated goal (marked by a white circle) alongside Ralph perfectly unharmed.
Ralph is then let loose in different environments to steal Sam's flock from him one sheep at a time assisted by Daffy who appears in different theme appropriate disguises. Several of the levels are based on classic Looney Tunes cartoons such as the level based on Chuck Jones famous hunting trilogy or a stage based on the backdrop of Wile E. Coyote and Road Runner shorts. During a later level, one of the goals is painted on a pirate ship's sail. Ralph uses a cannon to launch the sheep up to the goal and accidentally into outer space. The sail is ripped off the mast and surrounds Ralph which means that this scenario did not violate the rules for both the sheep and the wolf had been within the boundary of the goal. Ralph then continues to steal Sam's last remaining sheep and returns to the studio as the winner of the game.
Marvin the Martian crashes through the studio ceiling and informs Ralph that the sheep he launched into space crash landed on Planet X and released an army of Marvin's Instant Martians. Marvin has already captured most of the army but there are still a group of ten who have managed to isolate themselves in dangerous locations. Marvin has his sidekick and pet dog K-9 grab Ralph and the three fly back to Planet X. Marvin provides Ralph with the necessary Martian catching equipment and he goes off to capture the remaining ten Martians, knowing that without doing so, Marvin will not return him to Earth. After facing several dangers, Ralph succeeds in trapping the last of the Martians and Marvin gladly returns him and the sheep to his home.
Ralph takes the sheep inside and finds there is a lucky goal painted in the middle of the floor. He carries the sheep into the goal where it reveals itself to be none other than Sam who is about to beat Ralph for thieving his flock. It is at that moment that Ralph's alarm clock rings and he awakes in his chair, meaning that the events of the game were all a dream. Ralph then walks outside and meets Sam at the time clock ready to start another day of work.
