Is there a way to convert an old Star Wars character (d6 system) to Edge of the Empire?
The West End Games Star Wars RPG (d6) ruleset and the newer Fantasy Flight Games Star Wars RPG (Edge of the Empire, Age of Rebellion, Force & Destiny) vary quite drastically in many, many, ways.
You can keep the same character personality in mind but will need to go through the character generation process from scratch using the Edge of the Empire rules and selecting the options you feel fit the character best.
There is no official way to do this.
Also, while Genesys and the FFG SW RPG line are practically the same core system, there are some nuances. I will attempt to write this from either angle as both are useful to know.
Ultimately you're probably best off just making a character in EotE/Genesys that is as close to your d6 Star Wars character as possible, by spending xp as normal and having similar base gear.
To attempt it, you would need to do 5 things:
1. Identify Species/Archetype
Probably the easiest step. I would advise looking up an equivalent species in the FFG Star Wars RPG, and then use that exact profile. It generally should be the same for both Genesys and the SW RPG line. In the case that the SW RPG species contains wording that doesn't map to Genesys (I'm really not sure what that might be), just make an on the spot ruling for a similar effect.
2. Identify Career
In Genesys, a career consists of 8 skills that this particular character is more effective at training. I will admit I don't know the d6 Star Wars system, but this would just be identifying the 8 skills your PC is most capable with and marking these as career skills.
If porting to the SW RPG, this is a selection of a single career as presented across all of the books, as well as a single starting specialization from within that careers options. This is mainly a matter of looking at what your character is good at/started as, and selecting the closest match. E.g. a Han Solo like character would choose the Smuggler career, with the Scoundrel specialization.
3. Finish out Character creation normally
At this point you've basically made a starting PC in EotE/Genesys. Follow the rest of the steps in the sections of the book to wrap this up (spend the core XP on attributes, starting wealth, etc.). If playing the true Star Wars line, this also means picking up Obligation/Duty/Morality, as appropriate to the core book you're using. I wouldn't modify this process.
4. Add XP and spend it
This is where porting will get tricky, as I assume you're attempting to port an advanced SW d6 character and not simply make a new one. Frankly, I'm not sure what a good measurement would be equal to. Probably your best bet would just be to use the "Knight Level Play" option presented in the SW Force and Destiny line (start play with an extra 150xp and 10k credits or a lightsaber).
On spending xp, this is a matter of spending it to make the new character feel as close to the d6 RPG as possible. So advance skills or buy talents and specializations to most closely match what your old character was.
5. Determine wealth and buy gear
I would just give the character the exact EotE version of the ship your d6 RPG character has. The FFG system has a pretty solid array of Star Wars ships, so it should be in some book somewhere. Also this ship profile is almost exactly how Genesys does it, just consolidate its defense stats.
As well, give them the same equipment. Determine if a weapon is a blaster pistol/carbine/rifle the PC has and give appropriately Armor is much simpler as well. Find the closet version of armor in EotE core and give them that. If a lightsaber, use either EotE's base lightsaber, or use the Force and Destiny rules to come up with the appropriate crystal for the saber. I'm uncertain how credits map between systems. You really might be fine just saying you have the exact same amount of credits, but you might want to compare prices and adjust normally.