My baby is 12 weeks old and has begun to roll from his tummy to his back. He sleeps in a cot in a sleeping bag with his arms in. Do we need to allow him to have his arms out now? He is not yet rolling from his back to his belly.

Most babies will be rolling over by 4- 5 months. Some earlier, some later
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their tummy.
This is not something that needs to be stopped. It is important to make her new environment as safe as possible.

It is time to stop swaddling (or swaddle suit). He needs his arms free to roll safely.
Also ensure that the mattress is firm & flat & there is nothing soft or loose in the cot.
Always place baby on back to sleep.
Increasing tummy time when awake is also helpful.

Red Nose has the following information now that your baby is starting to roll.

Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over