Income to you is reported on your income tax return.  Why would you put that in an account not accessable by you ?

I didn't put it there. It was an online trading account. I was scammed.  I don't have access to the account unless I pay a fee.  The "account manager" is now saying I owe her money and threatening to report to the IRS if I don't pay and is refusing to close the account. So I'm just wondering if I am responsible for the funds.

DO NOT pay anything to a scammer ... even if you pay the ransom the account probably will not be released.  A conman will always try to squeeze out every penny they can ... first file a police report and admit you got scammed and  see the info here :  https://www.usa.gov/stop-scams-frauds

If you report the scam there may be a chance to recoop some of your loss or at least get the satisfaction of turning them in.  

And if this is truely  a scam then there are no profits or losses to report ... there will be no tax reporting form issued... the money is gone and they are trying to milk you for more.  

"It was an online trading account."

With what broker?

you probably gave her your SSN to set up the account. assuming she is truly a scammer and something else isn't going on that was unmentioned you could find yourself the victim of identity theft.  file form 14039 with your tax return.   also, you can't deduct the money you gave her for "investments".