I think you mean "it made my blood run cold" ("run," not "turn.") It means the same thing as "sent a shiver down my spine" and "it gave me gooseflesh" or "it was blood-curdling." It means a sensation of fear or horror or dread so intense that it evokes a physical response, resembling the response to a sudden chill. For example, the (comic) poem, "The Cremation of Sam McGee," by Robert Service, begins: There are strange things done in the midnight sun By the men who moil for gold; The Arctic trails have their secret tales That would make your blood run cold; The meaning is that the things done would horrify you if you knew about them.

Arctic trails have their secret tales that would make your blood run cold’

Have you ever been suddenly horrified by something in a way that suddenly made you feel frozen with shock for a moment, and as if a chill had suddenly enveloped your body? In the next moment, you might start to feel the anger or bewilderment or terror that the situation calls for, but that initial shock can be a feeling of flash-frozen cold. "When I realized that those neglected toddlers had been locked in the closet since early morning, my blood ran cold." "I stared at the headlines in the paper, my blood suddenly running cold: my country had just invaded its old ally." "My blood ran cold as I stared at the empty sky where the twin towers had been." It can also mean the type of anger that, instead of being a rapid ignition of hot rage, is a slow smoldering of icy fire that can last for days or years. "His blood ran cold with unabated anger over all that he had lost in the war."

It means: "to make someone feel suddenly very frightened or worried"

It means to shock or horrify. For example, if a shocking news story breaks, someone may read it and be so horrified that they might say, that story has made my blood turn cold.