Use the page picker from wordpress menu creation page

I’m don’t know a way of re-using the page picker but you could achieve what you’re trying to do with the “Post Object” field type in the Advanced Custom Fields plugin.

The post object field creates a select field where the choices are
your pages + posts + custom post types. This field is useful for
advanced linking to another page / post.

http://www.advancedcustomfields.com/resources/post-object/

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