PHP, 26 Bytes

<?=-~log10(abs($argn?:1));

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

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PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn