The prime qualification for admission into the Royal Arch is to be a Master Mason, of at least four weeks standing, in a Lodge under the United Grand Lodge of England, or a Lodge under a Grand Lodge recognised by it.
As to the timing of when to join, the decision will depend on many factors. As stated, it is possible to be exalted (the equivalent of initiation) just 28 days after being raised, but for many Brethren this is perhaps too soon.
There are “traditionalists” who say that a Brother should wait until after he has progressed through his Craft Chair. However, while it is never too late to join the Royal Arch, such advice is unnecessarily postponing what should be one of the great joys in Freemasonry.
The essential requirements for exaltation are that a Brother should have come to terms with the lessons and teaching of the Craft, be at ease with the meaning of its allegories and be able to give the time to study and enjoy this new phase of his Masonic progression.
As in all other Masonic Orders you will need a Proposer and Seconder who are members of the Chapter in which you seek to be Exalted. If your Lodge does not have a Royal Arch Chapter attached to it, it will probably have an arrangement with a local Chapter. Check your Lodge summons which may give details of either the Chapter attached to it, a Chapter to which it recommends candidates or a Royal Arch representative within the Lodge.