If you think what I'm saying is 'ridiculous' Moaney, just ignore me. :)
OP, I assumed you were using a bit of hyperbole when you said your son was 'addicted to Twitter'. Teenagers are notoriously obsessive - they go through intense and sometimes quite long-lasting 'fads' - whether that's Minecraft, Dungeons and Dragons, football, Justin Beiber, a new girl/boy friend, or Twitter. 99.9% of the time, these obsessions pass naturally. Similarly, a large proportion of teenagers avoid homework and exercise
... It is perfectly possible that your son would be avoiding these even without Twitter. :)
If his 'Twitter addiction' is within normal teenage limits, then my view is that taking away something he enjoys is unlikely to make him happy or co-operative. IME, negotiation and compromise work much better than bans and crack-downs.
Bear in mind, too, that you want him to manage his own online time. He won't learn self control if you take control. It's better, really, to support him to work out how he can limit himself.
If I have misunderstood, and you mean that you think your son literally has an addiction, then I'd say you need professional advice. There is a lot of controversy about whether internet addiction actually exists, and many experts believe it doesn't in its own right, but rather is a symptom of more serious conditions like depression or OCD. Techniques like CBT can help, but he'd need proper assessment. A CAMHS professional (or similar) could also advise you whether total withdrawal is a good idea, or whether some other approach is better. Most therapies are built around giving more control to individuals, not less; so again, if you think your son has a real mental health problem, then I'd say taking his phone away from him is probably a bad idea.
Good luck with it, whatever you decide. :)