This question is raised from time to time. That Arthur was not a king during the period of his twelve battles is confirmed by the Historia Brittonum which gives him the title “dux bellorum” in the following passage:
“Then it was, that the magnanimous Arthur, with all the kings and military force of Britain, fought against the Saxons. And though there were many more noble than himself, yet he was twelve times chosen their commander, and was as often conqueror.”
This is not surprising since during these campaigns he may well have been in his early to mid-twenties. That he eventually became king of Dyfed is shown by his entry in HG 2.
The Annals of Ulster has the following statement under the year 467:
“Death of Uter Pendragon, king of England, to whom succeeded his son, King Arthur, who instituted the Round Table.”
Hennessy pointed out that this comes from only version B of the annals and was done in a later hand. This explains the anachronistic reference to an English king and a Round Table. The date for Arthur’s coronation is, clearly, incorrect and may have been the result of a copyist mistaking the date cccccxuii to be cccclxuii. This is close to that given by the Annales Cambriae for Badon as opposed to being much earlier providing evidence that Arthur attained kingship towards the end or soon after his twelve battles.
It has been pointed out that Arthur is not given the title “rex” in the AC. However, if the royals in version A are listed it shows this is not surprising.
Royals without their title:
516 arthur, 537 arthur, 537 medraut, 558 Gabran filius dungart, 580 Guurci, 580 peretur, 589 con stantini, 607 Aidan map gabran, 613 selim filíí cinan, 613 iacob filíí beli, 616 Ceretic, 616 Et guin, 626 Etguin, 626 run filius urbgen, 627 Belin, 629 cat guol laun, 630 Guidgar, 630 guin, 630 Catguo llaun, 631 catguollaan, 632 iudris, 657 Pantha, 658 Osguid, 662 broc mail, 665 morcant, 682 catgualart filius catguolaum, 722 Beli filius elfin, 750 teudubr filius beli, 760 dunnagual filíí teudubr, 775 Fernmail filius iudhail, 811 Eugem filius margetiud, 813 higuel, 814 Trifun filius regin, 814 grip huid filius cincen, 814 elized, 814 Higuel, 814 cinan, 816 Higuel, 825 Higuel, 842 Iudguoll, 844 mermin, 849 Mouric, 850 Cinnen, 864 duta, 873 mouric, 877 Rotri , 877 guriat, 878 Aed map neill, 880 rotri, 882 Cat guethen, 885 Higuel, 892 Himeyd, 894 Anaraut, 902 Igmunt, 903 Loumarch filius hiemid, 904 Rostri, 913 Otter, 939 Himeid filius clitauc, 939 mouric, 940 Ædelstan, 943 Catel filius artmail, 943 iudgual, 943 elized, 946 Cincenn filius elized, 951 cat guocaun filius ouein, 954 Rotri filius higuel.
Royals with their title:
547 mailcun rex genedotae, 595 Dunaut rex, 644 osuuald rex nordorum, 644 eoba rex merciorum, 669 Osguid rex saxonum, 704 Alch frit rex saxonum, 714 pipínus maior rex francorum, 716 Osbrit rex saxonum, 736 Ougen rex pictorum, 750 rex … talargan, 754 Rotri rex brittonum, 757 Edpald rex saxo, 776 Cenioyd rex pictorum, 796 Offa rex merciorum, 796 morgetiud rex demetorum, 798 Caratauc rex guenedote, 807 Arthgen rex cereticiaun, 808 regin rex demetorum, 808 catell [rex] pouis, 816 Cinan rex, 848 iudhail rex guent, 854 Cinnen rex pouis, 854 ionathan princeps opergelei, 856 Cemoyth rex pictorum, 871 Guoccaun … rex cereticiaum, 875 Dungarth rex cerniu, 900 Albrit rex giuoys, 909 Catell rex, 915 Anaraut rex, 917 Ælfled regina, 919 Clitauc rex, 928 Higuel rex, 942 Abloyc rex, 947 Eadmund rex saxonum, 950 Higuel rex brittonum.
There are 66 instances of royals not being given their title and 35 cases where they are. For the early period, say before the year 700, it is even more likely the title would not have been registered.
The poem Gereint fil[ius] Erbin refers to Arthur as:
“Amherawdyr, llywyawdyr llauur.”
“The description of him as ’emperor’ (ameraudur/amherawdur < Latin imperator) could reflect Geoffrey’s Arthur but not necessarily so.”
Nerys Ann Jones wrote of the poem:
“Most scholars believe that they [versions of the poem] probably belonged to a lost collection of poems about Geraint similar to the Llywarch Hen cycle, with possibly a prose element, and composed sometime between c.800 and 1100.”
“The use of the term amherawydyr (from Latin imperator) for Arthur is not likely to indicate the influence of the emperor figure of Geoffrey of Monmouth, as it was originally a military term for a commander-in-chief, and is used in the work of the Poets of the Princes, often in combination with llywyawdyr, for powerful leaders like the Lord Rhys, a ruler of Deuheubarth in the twelfth century, and Llywelyn ap Gruffudd, the last native prince of Wales.”
The two rulers listed by Jones tells us that the title does not preclude Arthur being a king.
The poem Kadeir Teyrnon refers to Cawrnur. He was one of Arthur’s counselors, see Cawrnur. The placename ‘Reon’ appears in the poem. Triad 1 tells us that ‘Penn Ryonyd yn y Gogled’ was one of Arthur’s tribal thrones.
The title of the poem could be translated either with a proper name as ‘The Chair of Teyrnon’ or as ‘The Chair of a Prince’. It would seem that the second interpretation is more likely, particularly since the following lines indicate the eulogy was directed to him:
“Arthur has been blessed
In harmonious song-
[As] a defence in battle,
Trampling nine [at a time].”
 Hennessy, W. M., 1887.
 Bromwich, R., Jarman, A.O.H., Roberts, B.F. (eds.), 2008, 48.
 Lloyd-Morgan, C., Poppe E., (eds.), 2019, 19.
 Bromwich, R., 2006, 1.
 Lloyd-Morgan, C., Poppe E., (eds.), 2019, 24.