Yes. Inasmuch as all that happens here below is subject to Divine Providence, as being pre-ordained, and as it were "fore-spoken," we can admit the existence of fate, because nothing hinders certain things happening by luck or by chance, if compared to their proximate causes, but not if compared to Divine Providence, whereby "nothing happens at random in the world," as Augustine says (QQ. 83, qu. 24).
Inquantum omnia quae hic aguntur, divinae providentiae subduntur, tanquam per eam praeordinata et quasi praelocuta, fatum ponere possumus, nihil prohibet aliqua esse fortuita vel casualia per comparationem ad causas proximas, non tamen per comparationem ad divinam providentiam, sic enim "nihil temere fit in mundo", ut Augustinus dicit in libro octoginta trium quaest.
What does not exist cannot be defined. But Boethius (De Consol. iv) defines fate thus: "Fate is a disposition inherent to changeable things, by which Providence connects each one with its proper order."
Quod non est, non definitur. Sed Boetius, in IV de Consol., definit fatum, dicens quod "fatum est inhaerens rebus mobilibus dispositio, per quam providentia suis quaeque nectit ordinibus".
The holy doctors avoided the use of this word, on account of those who twisted its application to a certain force in the position of the stars. Hence Augustine says (De Civ. Dei v, 1): "If anyone ascribes human affairs to fate, meaning thereby the will or power of God, let him keep to his opinion, but hold his tongue."
Hoc nomine sancti doctores uti recusaverint, propter eos qui ad vim positionis siderum hoc nomen retorquebant. Unde Augustinus dicit, in V de Civ. Dei, "si propterea quisquam res humanas fato tribuit, quia ipsam Dei voluntatem vel potestatem fati nomine appellat, sententiam teneat, linguam corrigat."
It has been said (Q115 A6) that what is accidental, is properly speaking neither a being, nor a unity. But every action of nature terminates in some one thing. Wherefore it is impossible for that which is accidental to be the proper effect of an active natural principle.
Dictum est enim supra quod id quod est per accidens, non est proprie ens neque unum. Omnis autem naturae actio terminatur ad aliquid unum. Unde impossibile est quod id quod est per accidens, sit effectus per se alicuius naturalis principii agentis.
We must therefore say that what happens here by accident, both in natural things and in human affairs, is reduced to a preordaining cause, which is Divine Providence. For nothing hinders that which happens by accident being considered as one by an intellect: otherwise the intellect could not form this proposition: "The digger of a grave found a treasure." And just as an intellect can apprehend this so can it effect it; for instance, someone who knows a place where a treasure is hidden, might instigate a rustic, ignorant of this, to dig a grave there.
Et ideo dicendum est quod ea quae hic per accidens aguntur, sive in rebus naturalibus sive in rebus humanis, reducuntur in aliquam causam praeordinantem, quae est providentia divina. Quia nihil prohibet id quod est per accidens, accipi ut unum ab aliquo intellectu, alioquin intellectus formare non posset hanc propositionem, "fodiens sepulcrum invenit thesaurum". Et sicut hoc potest intellectus apprehendere, ita potest efficere, sicut si aliquis sciens in quo loco sit thesaurus absconditus, instiget aliquem rusticum hoc ignorantem, ut ibi fodiat sepulcrum.
Consequently, nothing hinders what happens here by accident, by luck or by chance, being reduced to some ordering cause which acts by the intellect, especially the Divine intellect. For God alone can change the will, as shown above (Q105, A4). Consequently the ordering of human actions, the principle of which is the will, must be ascribed to God alone.
Et sic nihil prohibet ea quae hic per accidens aguntur, ut fortuita vel casualia, reduci in aliquam causam ordinantem, quae per intellectum agat, et praecipue intellectum divinum. Nam solus Deus potest voluntatem immutare, ut supra habitum est. Et per consequens ordinatio humanorum actuum, quorum principium est voluntas, soli Deo attribui debet.