SELECT p.*, x.*
FROM Projects p
CROSS APPLY (
SELECT TOP 1 *
FROM ProjectCategory pc
WHERE pc.ProjectID = p.ProjectID
ORDER BY NEWID()
) x
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden