Many, though by no means all, alphabetic small capitals are available in the Unicode range 1D00 to 1D7F. This block is known as Phonetic Extensions, and carries the introductory note
These are non-IPA phonetic extensions, mostly for the Uralic Phonetic Alphabet (UPA).
The small capitals, superscript, and subscript forms are for phonetic representations where style variations are semantically important.
For general text, use regular Latin, Greek or Cyrillic letters with markup instead.
As well as small caps (ᴀ ᴁ ᴄ), superscripts (ᴬ ᴭ ᵃ) and a few subscripts (ᵢ ᵣ ᵤ), the block contains various other typographically interesting characters. (I have no idea what they are used for in the Uralic Phonetic Alphabet — though see here.)
Here among the small caps you will find a ‘reversed N’, ᴎ, a sideways Ø (ᴓ) and a sideways ü (ᴞ). There is a ‘Latin letter voiced laryngeal spirant’ (ᴤ) and a ‘Latin letter ain’ (ᴥ).
Not everything here is from the UPA. There is also a special ligature ᵫ, which I can see appealing to English lexicographers who prefer respelling to proper phonetic symbols, as will ‘Latin small letter th with strikethrough’, ᵺ. There is also something called ‘insular g’, ᵹ, labelled ‘older Irish phonetic notation’.
Although they are not official IPA symbols, users of IPA will be happy to find here the lax high vowel symbols ‘with stroke’, ᵻ ᵼ ᵾ ᵿ: two of these are used in the Oxford Dictionary of Pronunciation, though the first, ᵻ, bears the Unicode warning ‘used with different meanings by Americanists and Oxford dictionaries’.
A further Unicode block, Phonetic Extensions Supplement (1D80 to 1DBF) covers various former IPA symbols from which recognition was withdrawn at the Kiel Convention in 1989: those for consonants with velarization ᵬ ᵭ ᵮ ᵯ ᵰ ᵱ ᵲ ᵳ ᵴ ᵵ ᵶ and palatalization ᶀ ᶁ ᶂ ᶃ ᶄ ᶅ ᶆ ᶇ ᶈ ᶉ ᶊ ᶋ ᶌ ᶍ ᶎ, and for both vowels and consonants with retroflexion ᶏ ᶐ ᶑ ᶒ ᶓ ᶔ ᶕ ᶖ ᶗ ᶘ ᶙ ᶚ. So we can now find in Unicode everything we might need in order to digitize the 1949 IPA Principles, Jones’s The Phoneme, and various English-language accounts of Russian phonetics.