This is false.
The 'availability of weapons' is not a primary cause of the rise of ISIS.
Take a moment to learn about the 'Arab Spring' [1], which started the Syrian civil war, which was the definitive geopolitical even that enabled the real rise what we now think of as ISIS.
First - ISIS has origins as more of a rag-tag group, of which there were very many in Syria for decades, but through a variety of opportunistic mergers, splits, allegiances forged and broken, ultimately became what it is. To say 'ISIS' was 'this or that' in 1999 wouldn't properly describe what it was.
The 'Arab Spring' was sparked in the Arab world ironically by the leaking of US Diplomatic Cables by Chelsea Maning, which by the way, largely showed US foreign core trying to do their jobs in a world full of corruption and stupidity. The cables revealed to the 'Arab Street' just how corrupt their leaders were - and protests were set off in Tunisia, Libya, Egypt, Algeria, Syria - and other places.
Various groups vying for power (i.e. Muslim Brotherhood) in the ME would use the opportunity to make a play for power.
The US was 'involved' everywhere, but mostly not to a material extent initially, except for Egypt obviously.
Syrian rebels of various kinds, rose up and civil war broke out with Assad against a variety of antagonists.
A weakened regime lost control over wide swaths of mostly empty territory in E. Syria near Iraq to what we now call ISIS.
None of this was materially caused by US occupation of Iraq.
Later, Barack Obama's will to 'get the troops out of the ME' inclined him to pull troops from Iraq. (FYI in retrospect even if we consider that the war in Iraq was a huge mistake itself, it was still probably a mistake to withdraw too early. It has echoes of Saigon).
Literally the day the US troops were gone, Shia Iraqi PM al-Maliki purged government of Sunni entities, pushed the Shia dominated federal Army into Sunni territory, setting of a soft-grade civil war.
The Sunni tribes, more fearful of Shia-laden government forces than they were of ISIS ... 'allowed' ISIS to come in from Syria and join up with sympathetic fighters.
As a side note: Iraqi Army units, surrounded by ISIS fighters in Sunni territory were told by Sunni tribes, that if they disarmed themselves, that the tribes would provide them safe passage back to Souther Iraq, essentially, the tribes would protect them from ISIS. But of course, they were double crossed. ISIS grabbed large Iraqi Army units, completely unarmed, and proceeded to execute them by the truckload in one of the worst massacres in modern history: literally rivers of blood forming from the lines of Shia Iraqi Soldiers beheaded one-by-one by ISIS.
And then of course ISIS had the run of Sunni Iraq until a very crude coalition of Iranian, US, Iraqi and Kurdish forces pushed them out, town by town.
Were the US to have left just a few battalions, literally 'behind the wire' in some empty plot outside of Bagdad, the US would have been able to maintain political leverage over al-Malaki in order to prevent him from his aggressive purge resulting in civil war, and the entry of ISIS.
It's important to remember that ISIS is 'the fault of ISIS' and their supporters. They're one of the worst stains of people on the historical record. Second, if there are more indirect issues we want to look at, it's the brutally uncivil, corrupt, selfish, power-hungry and irrational civil structures around the Middle East.
[1] https://en.wikipedia.org/wiki/Arab_Spring