Yes and you can also say, I watch what I eat.

This is an answer in California English a la Hollywood, my neck of the woods. Film actresses and starlets watch their figures, overweight people who are fighting the battle of the bulge watch their weight. Watching what you eat implies one is on a special diet; a person with diabetes or who is allergic to some food(s) watches what they eat. Paying attention to what you put on your plate is a nice way to say just exactly that and is probably post twentieth century in my opinion. The beauty of English is that it's not really one language, it's a mix of about ten and that means you have a wonderful selection of words with connotations and cultural implications. You can pick and choose your words from a great menu of vocabularies given or taken from other languages, making your words mean exactly what you want them to mean.

I'm paying attention to what i put on my plate

Yes you would say that :D, although if it is a reply to someone offering you food, you would say "No thanks, I'm watching my weight" as in it is something you are currently doing.

I am careful on what I eat