The short answer is yes. There is a way for a planet to capture an object without aerobraking or rockets.
The long answer is, It depends on what model you use to describe the system. And it depends on what you mean by capture. Engineers will use various simplifying assumptions to model gravitational systems. They will switching between models as needed to get practical results.
Using a restricted 2 body model:
If Mars was in an inertial plane and I was sitting at a distance of Earth's closest approach of 78.3 million km the escape velocity would only be 75mph(120kph).
If I were to drop a Satellite from this height it could form a highly elliptical orbit who's apogee would be 78.3 million km.
A more sophisticated model:
A more practical model would be to launch a satellite to earth escape velocity and then launch it on a Hohmann transfer orbit whose apogee just barely gets close enough to Mars that Martian gravity can capture it. The resulting orbit would be highly elliptical and this maneuver would require small navigational thrusts to get it just right. This maneuver can be broken down into 3 steps: 1 Earth-centered restricted 2 body model, one solar and one Martian. It is unlikely this would happen naturally with a random asteroid.
In a restricted 3 body model a planet and a moon can create a gravitational bottle that can capture asteroids naturally. These bottles have openings around the 2nd and 3rd Lagrangian points but only for satellites with a certain energy. These Orbits are chaotic however. A captured asteroid in this manner will have a half life before it is ejected through one of the holes or crashes into a planet or moon.
I suspect that most of the moons you see in highly circular orbits are formed from aggregate ejecta.
Here is a video:
I recommend reading this first