Yes, a non Catholic can confess to a Catholic priest. (The canon law point has already been addressed).
What the non Catholic is not generally eligible for is the full sacrament of Penance and Reconciliation.; thus the priest cannot grant you absolution.1 Our priest makes that clear to folks who are married to Catholics but who aren't of that denomination yet. It is OK to unburden your heart, but the full sacrament is only for those in communion with the Church.
Where this gets flexed a bit is during the Candidate process during the RCIA. A few weeks before being confirmed and received into the Church, the normal flow is that shortly before Easter Vigil, or other Confirmation event, a priest hears the Candidates' confession. (A Candidate is someone who received a valid Baptism from another denomination of Christian).
In the case of the non-baptized (Catechumens) entering the church, I've seen it done both ways.
The priest hears the Catechumens' first confession before baptism and confirmation.
Rely on Baptism washing away all stain of sin (which it does).
After the latter(2) way of doing this, the new Catholic is eligible for and encouraged to receive (due to any loss of Baptismal grace via mortal sin, and at least annually per the "Easter duty") the Sacrament of Penance and Reconciliation (Confession).
CCC 1446 Christ instituted the sacrament of Penance for all sinful members
of his Church: above all for those who, since Baptism, have fallen
into grave sin, and have thus lost their baptismal grace and wounded
ecclesial communion. It is to them that the sacrament of Penance
offers a new possibility to convert and to recover the grace of
justification. The Fathers of the Church present this sacrament as
"the second plank [of salvation] after the shipwreck which is the loss
The Vicar General in our diocese advocates for the latter form(2), but the priests in a given parish are allowed to do either. (Ours did the former(1) for years). As I understand it, the Canon Law that Andrew cites offers that flexibility.
The above applies to those entering the church; it is not technically applicable to your case unless you intend to leave the Episcopalian Church for the Roman Catholic Church.
Any Priest whom you approach with the request that he hear your confession will be able to give you (at the very least) pastoral guidance and assistance. If you feel it would be beneficial to you, all you can do is find a local Catholic priest and ask if he'll hear your confession.
1 Exception to the general rule: a non-Catholic Christian who is at the point of death (or in danger of death, per and makes a profession of faith to a priest, may also receive absolution via this sacrament. This is one of those edge cases. (844)
This answer was originally in this question, and was moved here.
To capture a point from two comments, and thus preserve them:
Not exactly “at the point of death;” but “in danger of death.” For
example, I would gladly hear the confession of a non-Catholic soldier
who was about to go on a dangerous mission, or a non-Catholic who was
in an area in which a dangerous epidemic had begun, and so forth
(provided he professes the Catholic faith in the sacrament,
obviously). In other words, the person does not have to be actually
dying to be in “danger of death.”
In other words, the impending death of the person need not be certain, or even probable—just reasonably possible. (This applies to all similar cases; for instance, in danger of death, a Catholic may go to confession to an Orthodox priest, or even a laicized Catholic priest.)
As ever, many thanks to @AthanasiusOfAlex