I would advise to stay away from any job sites that require people to post personal information out in the open. At least, it should only be visible to people/companies that are paying money to the job site for the privilege of getting this information. Anything less is simply not acceptable these days.
I would make a similar warning against sending personal details to people who post jobs. If they have a recognisable company e-mail like in this post, you are probably all right, but otherwise it is hazardous.
I presume that is a reputable company website? Where is it maintained? Remember European laws about data security are much stricter than in some other parts of the world, so a European site may be safer.
If you are satisfied about those questions, then it is probably the right place to enter your phone number.
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