Yes, you can you should be able to get the paperwork from your Coy AO/clerk, I have forgotten the form number, but you will need to complete the first part then the new gaining unit RA complete the second part gets lost in the post between you old / new unit and Glasgow, then Re fill out form resend it etc. (Not that I have done a transfer but you know that happens)!
As mentioned pretty straight forward. Only real problems if your hoping to keep rank, in that case it's possible but you may be expected to drop a rank or if you keep it - get qualfied within a two year time frame
Arrange yourself an interview with the RA Regt and explain you want to transfer, let your current Inf unit know and they should prep the paperwork for you. The form is an AFE 7547 Application for Transfer.