Dell Precision Tower 3620 + RTX 3060 - possible?

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?

Done, PSU is replaced
Only, I realized that original Dell PSU had no SATA cables. Instead, it had a separate cable connected to MB, and from MB it was divided into 2 sleeves for SSD and DVD.
My new replacement PSU had those SATA cables of course so I connected my SSDs via those cables. I removed the old (mentioned above) Dell cable from the case.
Did I do right? Or for some reason I need to keep that separate MB cable with Dell motherboards, to power up SSDs, not PSU cables.
I'll try to add a pic, Dell MB cable marked with white arrow

Is your new PSU a Dell PSU with 8-pin connection* for MB or aftermarket with 24-pin?  If it's 24-pin, you need a 24-pin to 8-pin adapter.  Not sure if mentioned already.  *Or Dell PSU with 24-pin connection.

The 3620 MB takes 8-pin + 4-pin connectors for power.  There's nothing plugged into the 8-pin socket in your photo.

After upgrade power supply, the SATA power cable from mother still works.  However, to keep from any confusion, use the SATA power cables from the new power supply.

As Brad pointed out, make sure to connect a 24-pin to 8-pin adapter cable.  Review my second post in this thread.

Thanks for replies!

Oh sorry, I had to be more specific.
The new PSU I got is not Dell. I did not mention its name because it's a Japanese brand and I am unsure how to pronounce it. But it's just a "standard" one, 650w since I am about to go with RTX 3060 

And yes I got 24-8 pin connector before installation, as it was mentioned here.

"There's nothing plugged into the 8-pin socket in your photo"
Right, that's because I unplugged it already before uninstallment. I just realized that "separate" Dell MB-SATA cable last moment, so decided to take its picture, just in case.

Anyway, I am using SATA power cables from my new PSU now, and guess that's the right thing to do :)

Thanks!!!

Looks like I can go with RTX 4060 Ti 16GB as well, since its recommended PSU is 500w and mine is 650w, now.
My only concern is the size, I found the smallest possible (I think) here
GeForce RTX™ 4060 Ti WINDFORCE OC 16G
Its size is L=201 W=120 H=41 mm
So I guess I won't need to break the chassis to remove SSDs
Overall to me, it looks both PSU and sizes are ok here, BUT! Would you please let me know if I am wrong. It's quite pricey to mistake... :)