I've seen many people play Sion as AD. I've also seen many of those people faceroll and got rocked in a lane. Here is my build that was worked for me several times(though I don't have the wins to show because I like playing other champions as well.)

Pros

Extremely hard hitter, even at low levels
Great survivability
Can stun
Can grant allied teammates healing

Cons

Slow early game
Can be easily harassed
Has to turret hug in a 2v1 lane

People may be wondering why THOSE runes?? Well, it's simple. The marks are there for armor pen, because AD Sion is and will always be an auto attacking champion. The seals are there for a little more health off the start. Combined with the flat health quintessences, I can usually start off a game with 650-700 health. The glyphs are for more CDR, for when the first stun didn't quite cut it.

I did the standard 21/0/9 masteries. Why did I go with AP instead of CDR? It's quite simple. Unless there is a jungler on my team, I often get blue whenever it's up. This makes it so that I will always have mana ad can stun more. I chose the AP mastery because from this, the stun and shield can it for a little more and block a little more.

The ones I recommend are Ghost and Exhaust. I will go over some of the other ones as well here.

Ghost - Hands down one of the best summoner spells in the game. It has amazing chasing and evading potential. I really don't know how many enemy champions would have gotten away had I not popped this. You should ALWAYS have this spell when playing this champion.

Exhaust - You may be wondering Ok, this guy's just dumb, exhaust isn't good anymore. Exhaust is there for two reasons. 1, it can save a teammates butt repeatedly. 2, during team fights, you can partially shut down their biggest threat.

Here are some spells you can also go if you want.

Teleport - I used to run Teleport/Ghost before I realized how useful exhaust really is. It can help you secure kills and save towers.

Cleanse - This spell I debated, having used it on my Tryndamere build, it's quite amazing. With the amount of stuns, slows, snares, and disables in this game, this really is an amazing spell for if the enemy team wont let you close the gap.

Flash - Another spell with awesome gap closing ability. I'm not a fan of this one, however, as it can't always help you out of a situation.

Ignite - This one I'm always on the fence about. While it can help secure kills and shut down certain champions like Mundo, I'm never really a fan of this unless I'm playing a champion like Katarina and have the improved version.

Here are some spells to flat out NOT get.

Clarity - Yes Sion has rather low mana and yes, I do not get any items to increase that in this build. Despite this, avoid this spell like the plague. It's not needed, it's a waste of a spell on this champion.

Heal - Just...just no. This build has plenty of life steal, so Heal will not be necessary.

Clairvoyance - You really shouldn't be taking this on Sion ever. Let a champion like Lux or Ashe take it so they can pinpoint their ult.

Fortify - Another spell that would be a wasted slot. Yes, it can guard your turrets, but, then again, so can you.

Rally - I still have yet to see this put into action well other than the video of a team killing a turret before minions spawn.

Revive - I have only ever taken this spell when I first started and when I was trolling on Twisted Fate.

Smite - You're not jungling, don't even think about it.

I've had many a person hate on me for not getting Atma's earlier. I'll explain why. I start off with the Vampiric Sceptre because I've tried starting with a Brawler's Glove and with the skilling order, it is more worth it to get the Sceptre first due to Enrage. First trip back, save up to 2k gold and then go back for your Berserker Greaves and Zeal. Next, rush an Infinity Edge. Not only does this give you crit AND damage, but it also increased your critical damage. That's a win-win. Next, Bloodthirster. This is what people have argued with me about. They say I should get Atma's before this. Here is my reasoning. Both give damage. While Atma's give more overall, Bloodthirster gives more Lifesteal AND damage overall. Lifesteal = survivability. Survivability = good. After BT and Atma's, finish off Phantom Dancer for the extra crit, attack speed and move speed. Lastly, Stark's Fervor if your team hasnt gotten it already. IF your team has, grab the Black Cleaver instead.

Seeing as this build is build around damage, I always max out Enrage first. It gives more than a B.F. Sword of damage off the start and while it takes health away every swing, is completely worth it. I put 1 rank in Cryptic Gaze, seeing as the stun is 1.5 seconds at all ranks, then just max out Death's Carress, getting Cannibalism whenever I can.

Keep in mind though, as with all Sion builds, this build is about farming. Whenever possible you need to be killing creeps in the woods or in the lane. Ideally, by level 18, you will have 3500 health from Enrage. Keep in mind, if you can reach this, it's game over. Your Atma's alone will be giving you 70 damage from your health, and you will be lifestealing insane amount of your more than moderate health.