You can but it can be tricky. Turing thin spindle stock requires a few tricks and or special tools. Image search "Spindle steady"
Your tools need to be razor sharp, use gouges not scrapers- a thin spindle won't suffer much pressure from the tool without chattering and whipping.
I'd try to turn an arrow on a lathe as a last resort, I'd try a plane or a router table first, and I've done many hundreds of hours of turning.
But, don't let me discourage you from trying, just be prepared for a challenge!