Is there a standard notation for poker games?
Yes there is a standard for notating poker games, though it's not so widely used. One of the reasons for this is doing it as a player in game is cheating, writing down the cards that have come out would be counting cards.

The card values are: 2-9,T,J,Q,K,A in standard notation.

Suits can be noted, with the symbol of the suit (♠♣♥♦) or the first letter of the suit name (SCHD), though usually this is not bothered with as suits only matter in poker for the three flush type hands. Often is it just noted if a players hole cards are suited (s) or offsuit(o) - ATo would be an ace and a ten with different suits.

For community cards they are grouped and ordered as they would be on the table - 3 in the flop, 1 in the river then one for the turn.

Beyond that, notation for the players are BB(Big Blind), SB(Small Blind), BTN(button, the dealer), UTG (Under the Gun, to the left of BB and the first to bet) and CO(cut off, to the right of the button). Players if any between UTG and CO are notated by their distance from the closest of these, like  UTG+1 or CO-2.

Bets are noted by the dollar value of the bet, or by how many times it is the big blind (2.5x)