Kill everything else in the cave but the one you want with a giga. Then approach with ghili and bug repellent on FROM THE SIDE. He will not see you and you can tame at leisure. You can stay crouched next to him.
Take caution when in any cave or underground. The Araneo can climb walls and drop from the ceiling without warning. Their torpor inducing bite and slowing webs can put you in a helpless situation. Also keep in mind they tend to stay in groups. If you see one there is likely two or more somewhere nearby. I strong suggest and weapon with a flashlight attachment. A pump shotgun being my prefered caving weapon.
DONT put them in a trap, once they agro on a foundation they won’t de-agro.
Use fence foundations to make a trap if you have too.
If your able the best way is to use a Karkino to pick your desired spider up. Then put on your best gillie suit spray some bug spray and sit there feeding it