Any C-style for loop:

for (INIT; COND; POST) {
   BODY;
}
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Can always be rewritten as a while loop like this:

INIT;
while (COND) {
   BODY;
   POST;
}
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So your loop can be written as:

$j=1;
while ($j<=10) {
   print "$j\n";
   $j++;
}
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However, in Perl there are more idiomatic ways of writing it. For example:

print "$_\n" for 1..10;
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Or, if you've got a recent version of Perl, and enable the "say" feature:

say for 1..10;
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