That isn't currently possible, however, when Scratch 2.0 comes out, you can use a cloud list to track highscores.
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You'll have to wait for scratch 2.0 if you want to do a system where it will remember highscores. In scratch 2.0 there will be a type of variable called cloud variable, this type of variable is stored in the cloud rather than in your file and can remain even when your project is not running, this way you could make it so that it only changes it if score is higher than highscore or (i'm not sure about this one) you might be able to make cloud lists and then add all scores when the game ends to the list.
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I don't think you can do it yet on the online beta (http://beta.scratch.mit.edu/projects/editor/?tip_bar=home) but I may be wrong, or it may be updated in the future or you may have to wait until it is downloadable.
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At the start of the game use the hide variable block on the varibale 'score' and then at the end of the game use the show variable block to show it again.
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