It's not perfect but I came up with a new way of building a staircase, I say it's not ideal as you have to run to climb the stairs. However it's perfectly servicable and takes up less room then most solutions. A full video guide can be found at the bottom of this page.

Required Materials
 | Wood Can be gathered by chopping down all trees. |
 | Core Wood Can only be obtained from chopping down Pine trees in the black forest. |
Instructions
I started with a 3 x 3 flat floor and stood a 4m Log Pole on the corner of 4 of the floor panels.

I then built a Wood beam 2m and clipped it to the bottom of the upright. This burries half of the beam under ground making it so you can walk up it.

Next select a Log beam 2m and spin it which ever way you want the staircase to go by one notch. Aim about 1/3 of the way from the upright pole along the Wood beam 2m and it'll clip in place.

Again select a wood beam 2m rotate it in the same direction by one notch again, Aim at the 4m log pole just above the wood beam 2m and it'll clip again.

Keep repeating the process, switch between Log beam 2m and Wood bean 2m rotating a click each time and the spiral staircase will increase in height in no time.