Send your resume. Your address, phone number, name, work history and education history are all there. If they are asking for any additional personal information, share that you are happy to provide those details to potential employers for the purpose of a background check, etc.. If the recruiter wants to complete a credit check or background check as well, share that you are willing to provide personal details directly to the agency completing the check.
You should be forthcoming with information related to your work and education, but be guarded about personal information.
Best of luck with the job search!