Nope, but you can make them into a pkg file and install it as an app for the ps3, if you have a backwards compatible ps3 you can just mount them via multiman and webman, just look up how to make a ps2 game into pkg and you should find what youre essentialy looking for, i believe the software was called "ps2 ps3 tools" but i cant remember since its been a while since i did the process, the If you want to play PS2 games of your PS3, then you need to make sure you buy the right model. 
 Gamers could previously download PS2 classics and save game to the PS3 drive, but Sony closed the PS3 store in 2018. Yes and no. RPCS3 is simply emulating the PS3, and since the PS3 didn’t support out of the box backwards compatibility, it makes sense neither does its emulator. However, PS2 titles that were released on the PS Store can be played through the emulator. Simply extract the game from your device’s internal storage and follow the method Lukie Games. You'll find tons of retro games on Lukie Games, ranging from the NES to the Xbox. Lukie Games tests every single game on the site, so you'll almost never get a defective one. It also has a convenient 90-day return policy if anything goes wrong (or if you just hate the game). I have a PS2 but I want to play it on my PS3 because I want them all in one place instead of going through physical disc mess. Besides, I don't have a working controller for my PS2. Would you mind sending me one? That would actually help me. It may still be of some help to you, even though it's a different emulator than what is used for burned PS2 backups on BC PS3 models. If nothing else, it's a list of what PS2 games are compatible on any given PS3 with CFW or HEN - backwards compatible or not. PS2 Classics Emulator Compatibility List. 3. Place a ps3 slim into the ps2 console slot. 4. Hold down L1+R1+L2+R2 until you see an option for “playstation 2”. 5. Select that option and hit X or O to start playing! 6. Turn off the system by holding down L1+R1+L2+R2 again, then select “quit without saving” before turning off power button on main menu screen. Contents [ hide] In order to run PS2 games on PS3, we need to be signed PS2 classic placeholder. We gonna do a few steps and after that we can install our game without any issue. Put PS2 Classic Placeholder RAP file into Resigner Master>rifgen_master folder (Make sure you have you act.dat and IDPs.hex file inside Resigner Master>rifgen_master folder.) App Vay Tiền.

can you play ps2 games on ps3