How did you get the rooster sound out of your old Phone, i am trying to do this exact thing... i have a razr Maxx HD and the alarms on there are seriously lacking bite.
if you have a file manager app than copy your ring tones to the 'alarms' folder.
As for transferring the ring tones, either hook your old phone to your pc or use a cloud storage service such as Dropbox.
you could also email them to yourself.
If you are using the built-in Files app than copy the rings tones to the appropriate folder on the 'device storage' (the alarm, notification, and ring tone folders are already there)