No, not true.
That's a direct copy of a biblical story, Judges 7. In that story Gideon has to select his soldiers. He has too many volunteers. The Lord leads them to drink at a river. There the Lord selects for Gideon the 300 men he needs out of a multitude of soldiers. The 300 where the ones that rushed to the water and drank from their hands.
I haven't heard that story about Julius Caesar. It must be an apocryphal story, because that is not how Romans selected men for the army. The selection process was not that much different from what we practice today. Recruits were inspected, checked by medical orderlies or a doctor for physical and medical problems. How you drank water was not a requirement.
Something else that makes it very unlikely: Julius Caesar was far too important to be personally involved in the selection process himself. He just gave an order 'raise a legion in province x'. His officers would do what was required. He had too many jobs to manage to be bothered with such a tiny insignificant detail. His job was to appoint the officers and centurions. He knew them well, and most by name. It was the job of a centurion to go out and get recruits.