First get a list of the values in sorted key order. Note that @hash{ LIST } produces a list of the values corresponding to the keys in list.

my @values = @hash{ sort { $a <=> $b } keys %hash };
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Then clear your hash and assign the values using sequential keys:

%hash = ();
@hash{ 0..@values-1 } = @values;
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or do it all in place without a temporary array:

@hash{ keys(%hash), 0..keys(%hash)-1 } = ((undef) x keys(%hash), @hash
+{ sort { $a <=> $b } keys %hash });
delete @hash{ grep !defined $hash{$_}, keys %hash };
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Update:

@hash{ 0..keys(%hash)-1 } = delete @hash{ sort { $a <=> $b } keys %has
+h };
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almost works, but the keys(%hash) on the left is evaluated after the hash has been empty :(