$-1.6 \times 10^{-15}$ C
Step 1: The charge on a single electron is: \[ e = 1.6 \times 10^{-19} { C} \]
Step 2: The charge on the glass rod is given by: \[ Q = n e \] where $n$ is the number of lost electrons. Given that $n = 1000$, we get: \[ Q = 1000 \times 1.6 \times 10^{-19} \] \[ Q = 1.6 \times 10^{-16} { C} \]
Step 3: Since the rod loses electrons, it becomes positively charged.
Step 4: Therefore, the correct answer is (A).