I was so scared of hot foods like ginger causing issues, but my doctor assured me that a little bit of ginger in tea is completely harmless. Just avoid having too much of it, stick to one small cup.
Yes, ginger tea is perfectly safe and actually great for morning sickness. Just don't drink 4-5 cups a day, one or two cups of mild adrak chai is absolutely fine.
I used to have a small cup of ginger tea at my office desk to tackle the afternoon nausea. It's a great natural remedy, just keep the ginger quantity moderate.
I lived on adrak wali chai during my first trimester because my nausea was so bad! Looking back, it was a total lifesaver and completely safe, just don't make it too strong.