Can a practicing Catholic who joined a Protestant church still receive communion in the Catholic church?

Maybe. If upon deciding to join the Protestant church, the Catholic followed canonical forms and procedures, and renounced Catholicism, then the answer would be "No".

However, even if the Catholic joined a Protestant church, unless the Catholic renounced the Catholic church following the canonical forms and procedures, the Church considers that he or she is still a Catholic. Now, for a Catholic to have joined a Protestant Church, and partaken of communion there, would likely have been a mortal sin, meaning that the Catholic is not in a state of Grace, and is therefore barred from partaking of the Most Blessed Sacrament in a Catholic Church until restored to a state of Grace by having made a full sacramental convession.

Prohibited participation in sacred rites of non-Catholics (communicatio in sacris) is "to be punished with a just penalty," according to the 1983 Code of Canon Law (Can. 1365). The 1917 Code says:

Can. 1258 §1. It is not licit for the faithful by any manner to assist actively or to have a part in the sacred [rites] of non-Catholics

Thus, for a Catholic to receive Communion worthily in the Catholic Church after committing such a sin, he must first confess his sin to a Catholic priest (cf. 1 Cor. 11:27: "…whosoever shall eat this bread, or drink the chalice of our Lord unworthily, he shall be guilty of the body and of the blood of our Lord."). A sin of communicatio in sacris could be mortal, especially because we're dealing with very grave matter here (spiritual sins, such as sins against the faith, are graver than carnal sins).

No, because joining a Protestant church makes you a Protestant

You may not know this, but...

The sacraments of the New Testament were instituted by Christ the Lord and entrusted to the Church.

As actions of Christ and the Church, they are signs and means which express and strengthen the faith, render worship to God, and effect the sanctification of humanity and thus contribute in the greatest way to establish, strengthen, and manifest ecclesiastical communion. Accordingly, in the celebration of the sacraments the sacred ministers and the other members of the Christian faithful must use the greatest veneration and necessary diligence.

Canon 840

It is because the Church takes her sacraments so seriously that

Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others obstinately persevering in manifest grave sin are not to be admitted to holy communion.

A person who is conscious of grave sin is not to celebrate Mass or receive the body of the Lord without previous sacramental confession unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition which includes the resolution of confessing as soon as possible.

Canon 915-916

Somewhere in there, you'll have to convince yourself that going to a Protestant church is in fact a sinful act. But that's between you and God. (Maybe Germina's answer can help with that part)

However, remember there is the congregation and the priest who you are in danger of scandalizing. It's the priest's duty to know he's doing the right thing when giving you communion.

It is for the pastor to exercise vigilance so that children who have not attained the use of reason or whom he judges are not sufficiently disposed do not approach holy communion.

Canon 914 _{taken completely out of context, only used to illustrate the point}

So, if you think it's a problem, and you probably wouldn't have asked here if you didn't it probably is a problem. And if you're comfortable telling random Internet people, I hope you'd be comfortable enough to tell your priest!

Good luck and God Bless

Attendance at a Protestant church, even on a regular basis, does not detract from a baptized Catholic's Catholic identity in the eyes of the Church, and they are still obligated to follow the laws of the Church and the directives of their bishop and pastor:

Merely ecclesiastical laws bind those who have been baptized in the Catholic Church or received into it, possess the efficient use of reason, and, unless the law expressly provides otherwise, have completed seven years of age.

(Code of Canon Law, canon 11)

The Christian faithful, even in their own manner of acting, are always obliged to maintain communion with the Church.

(canon 209, sec. 1)

Conscious of their own responsibility, the Christian faithful are bound to follow with Christian obedience those things which the sacred pastors, inasmuch as they represent Christ, declare as teachers of the faith or establish as rulers of the Church.

(canon 212, sec. 1)

It is therefore not up to the person, nor up to their adopted ecclesial community, to determine whether reception of the Eucharist in a Catholic church is acceptable.

Now, in another answer, Geremia rightly points out that canon 1365 of the 1983 Code of Canon Law states

A person guilty of prohibited participation in sacred rites (communicatio in sacris) is to be punished with a just penalty.

However, as his source (New Commentary on the Code of Canon Law, published in 2000 by the Canon Law Society of America) indicates, exactly what constitutes "prohibited participation" is not clarified. The Church does absolutely prohibit concelebration of the Eucharist with ministers of a religious group not in communion with the Church:

Catholic priests are forbidden to concelebrate the Eucharist with priests or ministers of Churches or ecclesial communities which do not have full communion with the Catholic Church.

(canon 908)

as well as celebrating a marriage with such ministers:

there is not to be a religious celebration in which the Catholic who is assisting and a non-Catholic minister together, using their own rites, ask for the consent of the parties.

(canon 1127, section 3)

But there appear to be no other specific prohibitions. (I should note that Catholics are under certain restricted circumstances allowed to receive some of the sacraments from non-Catholics; but this permission doesn't apply to Protestant churches, the validity of whose sacraments the Church doesn't recognize.)

Thus, it's not quite clear when a particular level of participation in the rites of a Protestant church is "prohibited"; but for ecumenical reasons, some level of participation may be considered acceptable for particular purposes. As an example, if a person baptized in the Catholic Church becomes a minister in a non-denominational Protestant church, their commitment to, and perhaps their understanding of, the teachings of the Church is clearly questionable; whereas a Catholic who at the invitation of some Anglican friends attends a single Anglo-Catholic Compline service may be in a different position altogether.

The pastor of this person's parish is the one who has immediate responsibility for this person's spiritual care, subject to the the authority of the bishop (or other local ordinary). It is up to these two, ultimately, to decide whether a given Catholic in a given situation has violated the law of the Church or not, and whether in any case they are in a suitable condition for reception of the Eucharist.

The decision of whether a penalty such as that anticipated in canon 1365 is to be exacted will take into account a number of considerations, most of which are articulated in canons 1321–1330 of the Code of Canon Law. Importantly, canon 1321, section 1, states:

No one is punished unless the external violation of a law or precept, committed by the person, is gravely imputable by reason of malice or negligence.

Canon 1323 states:

The following are not subject to a penalty when they have violated a law or precept: ... a person who without negligence was ignorant that he or she violated a law or precept; inadvertence and error are equivalent to ignorance.

Finally, canon 1317 states:

Penalties are to be established only insofar as they are truly necessary to provide more suitably for ecclesiastical discipline.

Thus it is most probable, in most situations (unless, for example, the person has been repeatedly warned about this sort of behavior before), that no actual penalty will be assessed. What then will need to be done, to ensure that this person is in a fit state to receive the Eucharist?

The Eucharist is the actual physical reception of the Body and Blood of Jesus Christ; as such, it's (as an understatement) something very special. Geremia is quite right to quote St. Paul's statement:

As often as you eat this bread and drink the cup, you proclaim the death of the Lord until he comes. Therefore whoever eats the bread or drinks the cup of the Lord unworthily will have to answer for the body and blood of the Lord. A person should examine himself, and so eat the bread and drink the cup.

(1 Corinthians 11:26–28)

In order to receive the Eucharist in general, one must be free of any mortal sin:

A person who is conscious of grave sin is not to celebrate Mass or receive the body of the Lord without previous sacramental confession unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition which includes the resolution of confessing as soon as possible.

(Code of Canon Law, canon 916)

It is likely that the person's pastor will want to discuss with them the reasons they had for beginning regular attendance at a Protestant service, and also their reasons for wanting to return to the sacraments of the Catholic Church; there will likely be explanation required for the person to fully understand what it meant in the eyes of the Church for them to leave off practice of Catholicism, and what it means for them to receive the Eucharist, and why the Church teaches that they have gotten something wrong somewhere.

Once the priest is satisfied that they understand these things, and has led them to be able to make a good confession, there is no further obstacle to their receiving the Eucharist. Indeed, they may not be forbidden it: Canon 912 states: "Any baptized person not prohibited by law can and must be admitted to holy communion." (emphasis added)