I currently have money in the Acorns investment app and would like to withdraw it all to invest using TD Ameritrade. I'm worried that I will withdraw it, reinvest it using TD Ameritrade, then be charged tax on money that's still sitting in an investment account. Is it possible to transfer my money without being charged a capital gains tax since it's not income yet?
Yes, you can 100% transfer your assets between custodians without creating a taxable event. I've done this twice over the last few years. You are best served by contacting your new custodian, TD Ameritrade, to request the transfer paperwork. Typically, the outgoing custodian will charge a transfer fee and, depending on the custodian and generally the value of your assets, the new custodian will reimburse that fee. I've also had a fair amount of success getting the new custodian to "buy" my account with things like X free trades or something like that. To my knowledge you can't transfer your unit(s)/share(s) of traditional mutual funds (I've never tried), but your regular common stock and most other assets are transferable without selling or creating a tax event; in fact your cost basis data will be transferred too.
I don't know if Acorn (or Robinhood or any other investment "apps") wrap your assets in some strange thing to facilitate the low dollar trades and prevent the very normal transfer process, but TD will know what's possible.