After posting the negative answer below, I found one possible example: quă used as the feminine nominative singular or neuter nominative/accusative plural of the indefinite pronoun or determiner quis "any(one)". This form is listed in Bennett (91.), Allen and Greenough 149, Schmitz 1849. Gaffiot explicitly marks quă with a short vowel, which matches the usual length of terminal -a in words with these case/gender combinations.
Here is an example of the use of quă to mean "any(one)" (feminine nominative singular) in Punica by Silius Italicus:
du͞m sătǐ|s‿e͞st mŏnŭ|i͞ssĕ dĕ|a͞e. quo͞d |sī quă pŭ|dīca
me͞ntĕ vă|le͞t, sī |qua‿i͞lla͞e|sī sǐbǐ |co͞rpŏrǐ|s‿a͞dstat
co͞nscǐă, |ve͞l sō|lā sŭbĕ|a͞t pǐă |mūnĕră| de͞xtra.”
(XVII.30-32; bolding and scansion notation are mine)
Because this is in dactylic hexameter, it's clear that qua in the first line scans as a short syllable. The linked website explains "qua" as meaning "[ali]qua [femina]".
This is translated as follows in "The Other as Same: Non‐Roman Mothers in Silius Italicus’ Punica", by Antony Augoustakis:
[...] or the goddess may not be content with a mere warning. But if any woman has strength on account of her chaste mind, if any woman who stands here is conscious of a body unstained, let her, even with her right hand alone, undergo the pious duty.
(page 71, in Classical Philology, Vol. 103, No. 1 (January 2008), pp. 55-76, accessed through JSTOR)
but quă may be an enclitic
Quă is either largely or entirely restricted to occurring after specific words; namely, in sī qua as above (probably the most common context) and also after some other conjunctions such as nisi, nē, num or possibly after a relative word. Indefinite quis has a similar distribution; in fact, I haven't found a source that treats them separately. Because of the restricted distribution, some sources describe indefinite quis and quă as enclitics. I've asked a separate question to try to find out more about that: Does the indefinite pronoun/determiner “quă” only exist as an enclitic?
[This is my original answer, written before I came across quă.] Latin does not have any monosyllabic words that end in a short vowel when pronounced in isolation. This is my (re)formulation of a statement in "The Learnability of Latin Stress", by Diana Apoussidou and Paul Boersma, page 115. There is other literature that describes Latin as having a gap in words of this form, e.g. "The Quantitative Trochee in Latin", by R. Armin Mester, 1994, says "The crucial distributional finding in Latin (stated e.g., in Kurylowicz 1968 and Allen 1973, p. 51) is that monosyllabic words never consist of an open syllable with a short vowel" (page 20) and "Latin adheres to this minimal word requirement with remarkable strictness: There are literally no exceptions" (page 21).
A large number of monosyllabic words in Latin may scan as light syllables when followed by another word in certain contexts.
The most commonly encountered example is words ending in V̆C (such as in, ad, sed), which regularly scan as light syllables before vowel-initial words. In this context, the word-final consonant was apparently resyllabified into the onset of the first syllable of the next word. This resyllabification clearly occurred in poetry, and is believed to have also occurred in the ordinary spoken language, at least within a phonological phrase. Resyllabification of consonants before vowel-initial words also affected the weight of final syllables in words of more than one syllable.
Less frequently, you may encounter a monosyllabic word that in isolation ends with a long vowel scanned as a light syllable before another vowel. For example, you can find ŏ or quĭ scanned as short syllables before a vowel. This phenomenon seems to have a few names that aren't entirely synonymous: the term that I am familiar with is "correption". Correption of word-final long vowels seems to be described as a Greek-based practice in general, but for monosyllables it may have been normal in Latin:
Correption or "prosodic hiatus" of monosyllables is a special case, not confined to Graecizing contexts. It probably reflects actual *pronunciation. It is regular in drama, e.g. Plaut. Merc. 744 nam qui amat, quod amat si habet, id habet pro cibo. It occurs occasionally in Lucretius, Catullus, Virgil, and Horace's Satires. The non-elision of monosyllables ending in -m occurs with a similar distribution and should probably be counted in this category [...]
("hiatus", The Oxford Classical Dictionary, edited by Simon Hornblower, Antony Spawforth, and Esther Eidinow. This entry cites the following references: "M Leumann, J. B. Hoffmann, and A Szantyr, Lateinische Grammatik (1977), 1. 122-3; H Drexler, Einführung in die römische Metrik (1967); W. Lindsay, Early Latin Verse (1922), ch. 3; D. S. Raven, Latin Metre (1965)"; the contributor is given as Jonathan G. F. Powell.)
Elision of the long vowel (resulting in a reduction in the number of syllables) is an alternative possibility even for monosyllables, though. You can see more examples and discussion of conditioning factors for elision vs. correption in the article "Elision and prosodic hiatus between monosyllabic words in Plautus and Terence", by Kanehiro Nishimura (2016).
There are monosyllabic enclitics (not independent words) that (usually) end in a short vowel and scan light when followed by a consonant-initial word: -que, -ne, -ve.
Some words have phonologically clitic contracted forms that are non-syllabic: for example, est has the contracted form 'st, which is phonologically dependent on the previous word. (For more details on the contraction of forms of esse, see Terence and the Verb 'to Be' in Latin, by Giuseppe Pezzini, 2015.)