Voir par exemple cette liste de termes d’argot proposée sur un forum.

Comme a noté Toto, je ne connais pas non plus d’argot pour « aujourd’hui », mais je vois souvent sous forme de SMS « auj » et comme a dit Random, « ajd ».

Les mots familiers ou d’argot portent rarement sur des termes techniques ou précis comme le temps, des mesures. Ils portent sur des qualificatifs (avec tout ce que cela peut avoir de péjoratif), sur des verbes (toubib, d’origine étrangère en fait), et sur des mots communs d’usage très fréquent (bagnole, …).

en revanche, on peut trouver des diminutifs, pour simplifier: à + , pour à plus tard.

si on cherche une forme simplifiée, on pourrait employer des termes anglais plus concis:

• today
• now (approximatif)

Si on veut être subtil, on peut essayer hui (pas certain d’être compris).

There is no need for slang as many abbreviations are typical, such as auj. for aujourd’hui (see others), and people have been wondering about those before mobile and such. The period is required at the end.

Though “aujourd’hui” is quite long for sure, it is very spread and there is no real alternative to it. Get used to type it, because you’ll do it a lot.

• “auj.” could work, but this abbreviation is a bit short, and isn’t used that much, so you would need a context that makes really clear you’re referring to a day.
• I’ve never read “ajd.”. Don’t use that.
• You could use “today”, but I’m advocating against Frenglish.

Il n’existe pas d’équivalent à aujourd'hui dans la langue Française, néanmoins vous pouvez remplacer le mot par actuellement / maintenant (now).

Par SMS l’utilisation de ajd reste rare, auj trés rare (jamais vu).

There are no short forms for aujourd’hui that are commonly used (to put in contrast with the word aprèm short for après-midi, afternoon which is very common).

If I were to send “auj./ajd” in a text message or an email to a friend from my engineering school, or a colleague even in a non-professional context, I’m not sure they will understand it instantly, so I’ll use the entire word anyways.

If your chat room’s users commonly use three, two or one letter words that may include digits (example: 2m1 t ou), go for it.

Personally I didn’t know auj. even existed, but if I’d seen this in a mail I’d probably take several seconds to read the context and understand what it meant in retrospect. @cccg03’s answer links to an “internet slang” resource with lots of such abbreviations, and even though I grew up with mobile phones when I was a teenager there are only about ten words in there I recognize, and for some I understood a completely different meaning (we use pj at work but it means pièce jointe, email attachment, not petit joueur).

Be careful of who the recipient of your messages is, if you use abbreviations or slang the recipient doesn’t understand immediately, it defeats the purpose.