This can be done easily with straight canon.
The DMG p.268 says:
Intelligent items can actually be considered creatures because
they have Intelligence, Wisdom, and Charisma scores. Treat them
as constructs (see page 307 of the Monster Manual).
There is no reason why a construct could not be crafted into the form of a sword, or a staff, or even a spoon. Unlike normal constructs, Intelligent items don't usually have STR or DEX scores, unless they have some sort of permanent Animate objects effect on them OR they were crafted with parts that could function as arms and hands, legs and feet, so that aspect will need to be taken into consideration at character creation time.
Furthermore, the Monster Manual allows Intelligent items to progress and gain construct hit dice:
Increased Hit Dice: Intelligent creatures that are not humanoid in shape, and nonintelligent monsters, can advance by increasing their Hit Dice. Creatures with increased Hit Dice are usually superior specimens of their race, bigger and more powerful than their run-of-the-mill fellows.
Buried in the Monster feats section of the SRD is the text of the Craft Construct feat:
Craft Construct [Item Creation]
Craft Magic Arms and Armor, Craft Wondrous Item.
A creature with this feat can create any construct whose prerequisites it meets. Enchanting a construct takes one day for each 1,000 gp in its market price. To enchant a construct, a spellcaster must spend 1/25 the item’s price in XP and use up raw materials costing half of this price (see individual construct monster entries for details).
A creature with this feat can repair constructs that have taken damage. In one day of work, the creature can repair up to 20 points of damage by expending 50 gp per point of damage repaired.
A newly created construct has average hit points for its Hit Dice.
There is no limit on the shape of the construct, or even materials used. For example the packmate is a mobile chest or trunk, while the arbalester is a walking crossbow. There are swarm, serpent, and arachnid types covering your creepy-crawly body shapes, steed types which are quadrupeds, and even incorporeal types which are definitely not made of flesh, rock, or metal. I recall that there is a magma type and a force type as well.
For a detailed listing of all kinds of constructs, I suggest the Mechonomicon. You can even find Boots, Book, and Boat type constructs!
Constructs also have a fair number of abilities based on their type, which may or may not be considered appropriate for a 6th level character as they result in a fairly high Level Adjustment, listed in part here:
- No Constitution score.
- Low-light vision.
- Darkvision out to 60 feet.
- Immunity to all mind-affecting effects (charms, compulsions,
phantasms, patterns, and morale effects).
- Immunity to poison, sleep effects, paralysis, stunning, disease,
death effects, and necromancy effects.
- Cannot heal damage on their own, but often can be repaired by exposing them to a certain kind of effect (see the creature’s description for details) or through the use of the Craft Construct feat (see page 303). A construct with the fast healing special quality still benefits from that quality.
- Not subject to critical hits, nonlethal damage, ability damage,
ability drain, fatigue, exhaustion, or energy drain.
- Proficient with no armor.
- Constructs do not eat, sleep, or breathe.
One possible solution (if this is considered a problem) is to use the Living Construct type from the MM3 instead of the Construct type, which would remove some of the problem abilities that most PCs would not come easily by:
- Unlike other constructs, a living construct has a Constitution score. A living construct does not gain bonus hit points by size but gains (or loses) bonus hit points through a Constitution bonus (or penalty) as with other living creatures.
- Unlike other constructs, a living construct does not have low-light vision or darkvision.
- Unlike other constructs, a living construct is not immune to mind influencing effects.
- Immunity to poison, sleep effects, paralysis, disease, nausea, fatigue, exhaustion, and energy drain.
- A living construct cannot heal damage naturally.
- Unlike other constructs, living constructs are subject to critical hits, effects requiring a Fort save, death from massive damage, nonlethal damage, stunning, ability damage, ability drain, and death effects or necromancy effects.
- Unlike other constructs, a living construct can use the run action.
- Living constructs can be affected by spells that target living creatures as well as by those that target constructs. Damage dealt to a living construct can be healed by a cure light wounds spell or a repair light damage spell, for example, and a living construct is vulnerable to a harm spell. However, spells from the healing subschool provide only half effect to a living construct.
- A living construct responds slightly differently from other living creatures when reduced to 0 hit points. A living construct with 0 hit points is disabled, just like a living creature. He can only take a single move action or standard action in each round, but strenuous activity does not risk further injury. When his hit points are less than 0 and greater than -10, a living construct is inert. He is unconscious and helpless, and he cannot perform any actions. However, an inert living construct does not lose additional hit points unless more damage is dealt to him, as with a living creature that is stable.
- Can be raised or resurrected.
- Does not need to eat, sleep, or breathe, but can still benefit from the effects of consumable spells and magic items such as heroes' feast and potions.
- Does not need to sleep, but must rest for 8 hours before preparing spells.
Advancement becomes the next issue. Should your player character madly desire to be an exact replica of an Intelligent item as per the DMG entry, including the tables of lesser, greater, and dedicated abilities, then you'll have to figure that out. In such an extreme case, I suggest using the Table 7-30: Item Intelligence, Wisdom, Charisma, and Capabilities on DMG p.269 as if it were an Intelligent Item "class" instead, with each entry being one or two or even more Hit Dice per "level".
Should the player instead prefer class levels, your job becomes easier. They start off with as many HD as you feel appropriate for their item type - For example, if they choose to be a magic sword, then assign as many Construct (or Living construct) Hit Dice as would be needed to match the typical Hit Points of a normal sword; and any Level Adjustment that you feel appropriate for any special abilities they may have. After that, they simply advance by character class.
As a side note, and as a personal favorite, the Psionic power of Steelsteal allows one to leave their body and possess a bladed weapon. (If you check out the link, you may need to 'select all' in order to see the text, it displays as white on some browsers.) I have a build based around this concept located here. (Do a keyword search for "steal steel" and click on the spoiler tag of #8 to reveal the build.) The basic concept of the character is someone who specialized in Astral Constructs and passes herself off as a magic item to everyone else. I even figured out a method to store her body safely while she is off adventuring as a dagger.