If male, you should be able to. If female, I don't know. As in, I literally don't know.
I'm a former cross country runner. I went from ~135lbs to ~158lbs (so, a bit over 10kg) over a period of 3 months with minimal fat gain via a combination of lifting 3x a week and increasing calorie intake. I used a fair amount of milk, cream, eggs and protein powder in addition to other homecooked food.
What I would do if I were in your shoes is to make sure I'm hitting 1 - 1.5g of protein per pound of bodyweight every single day, and once that's in place, make sure I'm eating enough calories to gain weight. I take my weight every morning before a shower and track it on a whiteboard in the bathroom. Over the course of the week, you should be gaining 1-2 lbs of scale weight when everything is averaged out. If not, you should be eating more. If you're gaining weight faster than that, cut back.
Workout-wise, I'd cut out all cardio for now. I'd make sure I'm lifting using heavy compound movements 3x a week and increasing either the weight on the bar or the reps every single workout. Even if the weight increase is small (say, adding an extra collar to the bar), make sure something goes up every workout. You want a routine that's built around some combination of squats, deadlifts, overhead press, bench press, dips, pullups/pulldowns and rows.
My current routine, done 3x a week, consists of weighted dips, straight arm pulldowns, squats, overhead press and curls. I've used deadlifts, stiff-leg deadlifts, bench press, floor press, bent rows, and cable rows in the past... just not what I'm working with right now.
Assuming you're working hard in the gym, eating to grow, and getting sufficient rest, this should be basically all you need.