Hi, My baby boy is 4 days old and wriggles a lot in his sleep. He rolls right onto his side which makes me worried he'll turn over entirely. Given his age and he still wakes himself easily if his arms aren't swaddled, how should I be placing him in bed to prevent him rolling?

Most babies do not roll to tummy intentionally before 3 months; however, some babies do roll, especially to the side, at a very early age.

Is he in a bassinet?

Some babies do not respond well to wrapping/swaddling & prefer to have their arms free.         
Some babies like to touch their face or suck fingers when settling.
You could try settling him without any swaddle, or wrap with his arms out.
Are you using blankets?

Have you commenced tummy time yet when awake?
https://rednose.org.au/article/tummy-time-is-good-for-baby-because
Always place baby on the back for sleep.

You are not expected to wake during the night to keep checking on him.
However, there is nothing wrong with rolling him back if you see him on his side.

Red Nose does not recommend the use of sleep positioners.
Red Nose does not recommend positional products such as anti-roll devices and items that fasten a baby into a sleeping position.
Products that restrict the movement of a baby or a baby’s head should not be used.
https://rednose.org.au/article/is-it-safe-to-use-products-designed-to-keep-baby-in-a-particular-position