Yes, it's possible.  You must upgrade the power supply to 500w or higher in order to accommodate RTX 3060 power requirements.  With a PSU upgrade, users could use high performance graphics cards of their choices.

https://www.userbenchmark.com/System/Dell-Precision-Tower-3620/21304

@Chino de Oro​ Thanks!
I do not see RTX3060 in your link, though. Or I just miss it somewhere. 
And the main question is how to install that 500W PSU, I mean, is it available for 3620, at all? Dell always has those proprietary parts and I only heard about 365W or something, for 3620.

New link  https://www.userbenchmark.com/PCBuilder?searchTerm=precision%203620%20rtx%203060

For PSU upgrade, select a standard ATX power supply as your preference and use a 24-pin to 8-pin adapter cable.  See an installation instruction video here https://www.youtube.com/watch?v=rZxLJU0su8g

Be sure to use a good name brand PSU like EVGA, Corsair, Cooler Master, Thermaltake, just to name 4.

This shall probably be impossible, but - how about RTX 3090?
Any ways to install it to 3620 Tower? After PSU replacement, of course

Once you got the power requirements under control, just knock out the drive cage and you may be able to fit a 3090 in there.  Use blower style to remove heated air from the system.  There is a couple benchmarked for 3620 w/3090.

https://www.userbenchmark.com/UserRun/65480306

https://www.userbenchmark.com/UserRun/54104544

@Chino de Oro​ Wow!!! Thanks

May I confirm couple things

1. "knock out the drive cage" - is to remove those SSD drives, correct? Not the optical drive.
Guess I'll need to find some videos on where to place those SSDs, then :)

2. "blower style" - it's about the graphic board? "Blower style RTX 3090"? Both links you sent have pics of very "standard" 3090 board, but maybe it's just example photos not real ones.
Or "blower style" is some added separate fan, inside the cage.

The drive cage is the metal frame located on bottom of the chassis.  By removing it, you can add full length retailed video card.  See this video for visual process https://www.youtube.com/watch?v=Bjtpp-fIx_Q

See the difference between blower and open-air GPU cooler here https://www.howtogeek.com/365215/whats-the-difference-between-a-blower-and-an-open-air-gpu-cooler/.  Dell OEM RTX 3090 will do.

Wow thanks so much again. Such a great help.
Seriously, Dell should pay some members here, if they do not yet...

Removing drive case would be too intrusive for me, I guess. Kind of breaks the chassis, to a certain extent...
So after all consideration, I think I'll go with 3060. Not only cheaper but doesn't need a case removal (at least I haven't met such a condition yet).

Shall start searching for options, now.

I'd like to confirm just in case - is it correct that PSU size needs to be 85mm (H) x 150mm (W) x 140mm (L)?
Also, am I right that it can be smaller - but not bigger in any direction?