How long would it take to become an royal signals officer if I first joined as a soldier?

Hi, there is no clear answer to this question.
In order to go for a commission as a serving soldier you need to be recommended by your chain of command. You need to make it known that's what you're interested in doing. Some soldiers during Basic training have been highlighted as having potential officer qualities and have been highlighted to go the officer route really early on in their career. Once you have your recommendations and your commanding officer has completed the paperwork you then do exactly the same route as any potential officer (Army Officer Selection Boards etc). If you are successful you would go to RMAS as an Ocdt and commission as a 2Lt.
There is another way to commission - as Late Entry but you would need to wait until at least Sergeant and to commission into the Royal Signals you'd need to be a Warrant Officer.
I hope this helps.