The ITU-T E.164 standard defines a general format for international telephone numbers. Plan-conforming telephone numbers are limited to only digits and to a maximum of fifteen digits. The specification divides the digit string into a country code of one to three digits, and the subscriber telephone number of a maximum of twelve digits.
Source: Wikipedia
Suggestion for regex:
^(\+?[1-9])[0-9]{5,13}$
i.e. (group: ‘+’ optional + digits 1–9 as country code)(5–13 digits)