Loki's age is 1048 years old
According to the captions of the first Thor movie, the battle between the Jotuns and Asgardians take place in Norway, 965 AD. Around this time, Loki was born.
In Thor 2 the life expectancy was stated to be around 5,000. The average human life in developed countries from what I’ve gathered is approximately 82.
Therefore, in human years Loki is somewhere around 17.