Of course cats can carry diseases. So can dogs, ponies, rabbits, babies, toddlers, children, adults and any other living creature.
A super-cautious approach would be to check if your tetanus jabs are up to date (because tetanus is a soil-born organism and cats' paws tend to find their way into soil) but there's no greater chance of contracting tetanus from a cat than there is from accidental scratches from your dog's claws or from countless other sources.
Cats scratch and bite even the most loving of owners. (Er, sorry, 'owners' should, of course, read 'slaves'). But we don't all rush off to the nearest casualty unit!