Our group recently managed to acquire a Ballista, and our Eldritch Knight fighter was thinking of loading it and making it one of her bonded weapons. Is it possible for her to do so?
RAW - No, Ballista is not a weapon; RAI - Unlikely
The Eldritch Knight Weapon Bond feature states:
At 3rd level, you learn a ritual that creates a magical bond between yourself and one weapon. [...] The weapon must be within your reach throughout the ritual, at the conclusion of which you touch the weapon and forge the bond.
Nowhere else in the description of the feature does it provide a restriction to what kind of weapon it can be. Only that you cannot have more than 2 of them.
What counts as a weapon?
The important qualification for your DM to decide on is what counts as a weapon. A strict RAW interpretation would be that only items which appear in the weapons table, or are listed as "simple/martial melee/ranged weapon" in their stat-block, count as weapons.
Another question; Can the Eldritch Knight bond with his shield? says that you cannot bond with a shield since it is not a weapon. Even though you could use it as an improvised weapon. Improvised weapons that are similar to actual weapon can be treated as that weapon and should qualify for your feature. Any others would not.
In this situation, how do we classify a siege weapon? On page 255 of the DMG Siege Equipment we are given the stats for siege weapons. From there we have:
Ballista Large Object
Noticeable it is listed at an object despite being described as a siege weapon and having a ranged weapon attack. In contrast a heavy crossbow is listed in the PHB as a "martial ranged weapon". This means that by RAW you cannot use a ballista as your bonded weapon, as it is an object not a weapon.
For a RAI interpretation I think we get a clue from the next paragraph of the Weapon Bond feature:
Once you have bonded a weapon to yourself, you can't be disarmed of that weapon unless you are incapacitated. [...] you can summon that weapon as a bonus action on your turn, causing it to teleport instantly to your hand.
From this I think it is clear that the RAI is that the weapon should be something you can hold in your hands. Large siege weapons probably don't fall into this category. If a ballista were small enough to fit in your hands it is basically just a heavy crossbow and I would rule it has the same stats.