Yes, Christ ordained his apostles as priests.

wo author­i­ta­tive sources for the Church’s teach­ing on this point are the Cat­e­chism (always a good place to begin) and the Coun­cil of Trent. Here is the Cat­e­chism:

The Lord, hav­ing loved those who were his own, loved them to the end. Know­ing that the hour had come to leave this world and return to the Father, in the course of a meal he washed their feet and gave them the com­mand­ment of love. In order to leave them a pledge of this love, in order nev­er to depart from his own and to make them shar­ers in his Passover, he insti­tut­ed the Eucharist as the memo­r­i­al of his death and Res­ur­rec­tion, and com­mand­ed his apos­tles to cel­e­brate it until his return; “there­by he con­sti­tut­ed them priests of the New Tes­ta­ment.

And here is Trent:

If any one shall say, that by those words, Do this in remem­brance of me, Christ did not insti­tute the apos­tles priests; or, did not ordain that they, and oth­er priests, should offer His own body and blood; let him be anath­e­ma.

The Church gives Catholics no option to deny that Christ ordained his apos­tles to be priests.

•••

But that we may know the cer­tain­ty of what we teach, let us turn to the bib­li­cal text where Christ ordains his apos­tles. In Luke 22:19, at the Last Sup­per, he says to them: “This is my body which is giv­en for you. Do this in remem­brance of me.”

With those words, Christ ordains them as priests to offer the Eucharist as a sac­ri­fice.

Christ’s words, in the Greek text, are: τοῦτο ποιεῖτε εἰς τὴν ἐμὴν ἀνάμνησιν, touto poieite eis tēn emēn anam­nēsin. The words “touto poieite,” “do this,” have a sac­ri­fi­cial mean­ing. In Ear­ly Chris­t­ian Doc­trines, J.N.D. Kel­ly writes:

It was nat­ur­al for ear­ly Chris­tians to think of the Eucharist as a sac­ri­fice. The ful­fill­ment of prophe­cy demand­ed a solemn Chris­t­ian offer­ing, and the rite itself was wrapped in the sac­ri­fi­cial atmos­phere with which our Lord invest­ed the Last Sup­per. The words of insti­tu­tion, ‘Do this’ (touto poieite), must have been charged with sac­ri­fi­cial over­tones for sec­ond-cen­tu­ry ears; Justin at any rate under­stood them to mean, ‘Offer this.’ … The bread and wine, more­over, are offered ‘for a memo­r­i­al (eis anam­nasin) of the pas­sion,’ a phrase which in view of his iden­ti­fi­ca­tion of them with the Lord’s body and blood implies much more than an act of pure­ly spir­i­tu­al rec­ol­lec­tion. (196–197)

The rea­son this is impor­tant is because, to a first cen­tu­ry Jew, only a priest can offer a sac­ri­fice. If, there­fore, Christ tells his apos­tles “Do this”; and if the words have a pecu­liar­ly sac­ri­fi­cial mean­ing; then he is mak­ing them priests. He is is ordain­ing them.

That the first Chris­tians under­stood the Eucharist this way we know from the Didache:

Assem­ble on the Lord’s day, and break bread and offer the Eucharist; but first make con­fes­sion of your faults, so that your sac­ri­fice may be a pure one. Any­one who has a dif­fer­ence with his fel­low is not to take part with you until he has been rec­on­ciled, so as to avoid any pro­fa­na­tion of your sac­ri­fice [Matt. 5:23–24]. For this is the offer­ing of which the Lord has said, ‘Every­where and always bring me a sac­ri­fice that is unde­filed, for I am a great king, says the Lord, and my name is the won­der of nations.

•••

But we also know that the Greek word “poieite” (“do”) has a sac­ri­fi­cial mean­ing, con­nect­ed with the priest­hood, by virtue of the text of Exod. 29:38 in the Greek Sep­tu­agint. Speak­ing to the Levite priests of the Old Covenant, the Lord says: “And these are what you shall offer upon the altar: lambs of a year old, unblem­ished, two for each day per­pet­u­al­ly.” The Greek word trans­lat­ed “offer” (i.e., sac­ri­fice) is the very same that Christ uses in Luke 22:19: ποιήσεις. When Christ says “Do this,” he is say­ing, “Sac­ri­fice this.”

A sac­ri­fice is the act of a priest alone.

Just as in the Old Covenant, the Levite priests offered an unblem­ished lamb as a sac­ri­fice, so in the New Covenant priests offer Christ—the Lamb unblem­ished by sin—as a sac­ri­fi­cial offer­ing for sin.

When Christ says to his apos­tles at the Last Sup­per, “Do this,” “touto poieite,” he is using the very word for “sac­ri­fice” the Greek text of Exo­dus uses to describe the act of a priest.

He is ordain­ing his apos­tles.

For a more detailed bib­li­cal exe­ge­sis, take a look at Fr. James Swet­nam’s arti­cle in Pas­toral and Homilet­ic Review.