Yes it can be done, depending on the bike. You will hydraulic shifters to match your bike 8/9/10/11or 12 speed etc plus calipers to suit, flat mount or post mount with or without adapters depending on disc size. Giant do a halfway house using a mechanical to hydraulic converter. It would also help if you said which bike and existing brakes you have.
I went from sram shifters with mechanical BB5 calipers to Shimano 105 last winter. However, my frame is post mount, so I bought MTB Deore post mount calipers which work perfectly with the 105 levers.
Assuming this is a drop bar bike (given its the road section of the forum) yes its possible but you will need new shifters (compatible with any current kit you have i.e. 10spd / 11spd etc) and also new calipers.
Granted Hydraulic brakes are better than cable but given the cost of conversion I would instead opt for Spyre mechanical brakes instead - Way cheaper than converting to Hydraulic as you only need the calipers and given they move both sides of the piston (unlike basically all other cable discs) they have amazing power and modulation.
A properly setup set of Spyre's will be very nearly as good as Hydraulics and plenty good enough for a road bike.
Remember as well that a cable system is a fair chunk lighter than a Hydraulic setup and a hella lot easier to maintain/service.
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Granted Hydraulic brakes are better than cable but given the cost of conversion I would instead opt for Spyre mechanical brakes instead - Way cheaper than converting to Hydraulic as you only need the calipers and given they move both sides of the piston (unlike basically all other cable discs) they have amazing power and modulation.
A properly setup set of Spyre's will be very nearly as good as Hydraulics and plenty good enough for a road bike.
Remember as well that a cable system is a fair chunk lighter than a Hydraulic setup and a hella lot easier to maintain/service.
BR did a review of them here and they got a good score - https://www.bikeradar.com/reviews/components/brakes/disc-brake-systems/trp-spyre-mechanical-disc-brake-review/