What is the ruling on using a card that determines the gender of the fetus based on months of pregnancy in Islamic Sharia?

We do not know what you mean by "the card." If it is similar to the practices of fortune-tellers and astrologers who link days, months, and people's names to their influence on creation, or if it is a means of knowing the unseen, then this is forbidden polytheism (shirk). However, if it is a permissible and legitimate means, such as a scientific method for determining the sex of the fetus, then there is no objection to that.