Can my fork support disc brakes?
In order to fit a disc brake, you need a compatible fork and a compatible wheel, plus a compatible brake lever.

Your fork does have a disc brake mounting already designed in, it is an International Standard (I.S.) mount. Most mtb brakes now are Post Mount fittings so are fitted using a simple adapter. You can see the differences here or search around images.

To fit a disc brake you need a disc compatible wheel of the correct diameter (check the current size), the caliper and maybe a lever. If you have V-brakes now, you could add a mtb specific, cable-operated caliper to the existing lever with a new cable and housing. Alternatively you can get pre-bled hydraulic disc brakes, comprising the lever, caliper and disc, ready to use out of the box. N.B. there are two standards of disc mounting, 'six-bolt' and 'centre lock', match this to the new wheel hub.

Bear in mind that because you need a wheel change, changing to a disc brake could be expensive relative to the value of the bike (which is of course not always monetary). It's up to you to decide the best use of the money; that might mean upgrading this bike, or it might mean saving up towards a disc brake specific bike, new or used.

An interim upgrade could be a high quality brake of the same type you have; if it is a V-brake, good models are quite affordable and do make a noticeable difference over basic models. Also, with rim brakes particularly,  high quality brake pads noticeably increase performance for not a lot of money.