Transferring crypto between your own wallets and exchanges is not taxable
No. Transferring crypto between wallets and/or exchanges is not a taxable event. We like to use the metaphor that it’s like transferring a bunch of gold coins from your nightstand to the bank — the assets remain in your possession as usual, unchanged, just put in a different location.
The IRS clarified in their recent FAQ that transfers are not taxable, even if you receive an information return from an exchange (such as a 1099-K) reporting the transfers.