No. A financial transaction tax (which existed from 1914-1965) is different from capital gains. Capital gains is when the revenue of an asset is greater it's purchase price. I'm talking about a tax on Wall Street speculation, the proceeds going to the Social Security Trust Fund.
I like your idea for a tax revenue generator. But I still think SS needs to be altered.
How about this?
Some states have retirement plans for state workers that allow people to opt out of social security. These plans while originally tended to be more defined benefit have moved more towards defined contribution in order to prevent insolvency. These plans are very individualized and allow the person to even control the plan to some extent. You are still limited in choices to reduce risk, but you have some control so you can be more risky and have your plan invested more in stocks or be of lower risk and invest it in things like state bonds. You also can choose not to run it yourself and let it default to how the state board chooses. This will allow for much greater growth than social security and allows it to retain solvency longer.
If that alone is undesirable as there is risk of another economic meltdown like 2008, there could be a minimum defined benefit floor that is insured by the tax you are suggesting. This is the part that functions more like an insurance while the main plan functions more like an actual retirement plan. If your profile at retirement is above the floor then great, if not then it will be subsidized to meet the floor. I think most people, assuming they aren't unemployed for a significant portion of their adult life, would end up above that floor anyway.
Not sure if this would appeal to anyone or not, but I just liked how that state program offered more personalization.