Yes you can! Assetto Corsa supports H-Shifters on console, but only for cars that have a manual gearbox. If the car is a semiautomatic or requires paddle shifting, then the H-Shifter will be automatically disabled. You will then need to use the paddles to change gears.
** Important note! For certain wheels, such as the Thrustmaster T150 and T300, the TH8A shifter will only work in H-Mode when it is plugged directly into your PS4 via USB. When it is plugged into the DIN connector on the wheel base, it will *not* function in H-Mode, and will default to sequential shifting mode. **
The following list is all cars that have a manual transmission. Some of these cars may not yet be available in the console version of Assetto Corsa until future content is released.
Abarth 500 SS
Abarth 500 SS Step1
Abarth 595 SS
Abarth 595 SS Step 1
Abarth 595 SS Step 2
Alfa Romeo Mito QV
Alfa Romeo Giulietta QV
Alfa Romeo 155 Ti V6
Alfa Romeo GTA
Audi Sport Quattro
Audi Sport Quattro Step 1
BMW 1M
BMW 1M Step 3
BMW M3 E30
BMW M3 E30 step 1
BMW M3 E30 drift
BMW M3 E30 group A
BMW M3 E30 DTM
BMW M3 E92 Drift
Corvette C7 StingRay
Classic Lotus Cars 72D
Classic Lotus Cars 49
Classic Lotus Cars 25
Classic Lotus Cars 98T
Ferrari F40
Ferrari F40 Step 3
Ferrari 312T 1975
Ford Escort RS1600
Ford GT40
Ford Mustang 2015
KTM X-Bow R
Lamborghini Countach
Lamborghini Countach Step 1
Lamborghini Miura
Lotus 2 Eleven
Lotus Elise SC
Lotus Elise SC Step 1
Lotus Elise SC Step 2
Lotus Evora S
Lotus Evora S Step 2
Lotus Exige V6 S
Lotus Exige Scura
Lotus Exige 240 R
Lotus Exige 240
Lotus Exige V6 CUP
McLaren F1 GTR
Mercedes-Benz 190E EVO II
Mercedes-Benz C9
RUF CTR Yellowbird
Shelby Cobra 427 S/C