Yes, you can still get a no-contract or free prepaid cell phone from a couple of different companies online: Cricket Wireless and Metro by T-Mobile.
Earlier, a few other companies like Tracfone used to offer a basic phone free when you bought an airtime card at the same time, but those offers are no longer available. Those deals were still a bit suspect because you couldn't get a refund on the airtime if you didn't want the phone. Tracfone and Net10 do still offer a flip phone and a refurbished basic smartphone for $9.99 which is pretty cheap but not free.
Cricket Wireless offers a few free phones if you port your number and activate a $55 per month or $60 per month plan. There are cheaper unlimited plans out there so you may want to work out if the free phones are really worth it. Nevertheless, here they are.
For Metro, you only have to sign up for the $40 or $60 per month plan in order to get one of these 5G phones free via an "instant rebate" applied as a credit to your account.
That's a pretty good selection.