No, a stock trader in India cannot claim GST input for transactions done in the stock market.
GST Credit cannot be claimed by anyone except if they are rendering services where they are paying GST and this is as input to provide this service.
For example, Mutual Funds are paying GST on the cost charged to the corpus of the fund, and a contract note from a stockbroker is input to provide that service.
Except for PMS, AIF, and MF, no one can take GST credit.