Yes, canon law allows for getting married by proxy:
Can. 1104 §1. To contract a marriage validly the contracting parties must be present together, either in person or by proxy.
§2. Those being married are to express matrimonial consent in words or, if they cannot speak, through equivalent signs.
Can. 1105 §1. To enter into a marriage validly by proxy it is required that:
1/ there is a special mandate to contract with a specific person;
2/ the proxy is designated by the one mandating and fulfills this function personally.
§2. To be valid the mandate must be signed by the one mandating and by the pastor or ordinary of the place where the mandate is given, or by a priest delegated by either of them, or at least by two witnesses, or it must be made by means of a document which is authentic according to the norm of civil law.
§3. If the one mandating cannot write, this is to be noted in the mandate itself and another witness is to be added who also signs the document; otherwise, the mandate is invalid.
§4. If the one mandating revokes the mandate or develops amentia before the proxy contracts in his or her name, the marriage is invalid even if the proxy or the other contracting party does not know this.
