Can anisole be nitrated only with nitric acid?

Yes, it is possible to nitrate anisole (methoxybenzene) using not only concentrated nitric acid $(\ce{HNO3})$, but also dilute $\ce{HNO3}$ (Ref.1). The nitration of anisole in aqueous nitric acid in the concentration range 25.18-31.38 mol% at temperatures in the range $293$-$\pu{328 K}$ has followed the pseudo-first-order kinetics and the values of rate constant and activation energy have been reported.

The mechanism for the nitration is given as follows:

$$\ce{HNO3 + H3O+ <=> NO2+ + 2H2O} \tag1$$ $$\ce{NO2+ + ArH <=> encounter pair} \tag2$$ $$\ce{encounter pair <=> benzenonium ion ->[fast] products} \tag3$$

The author has stated that the activation energy of the rate determine step decreases with increasing acid concentration. This is a good indication that the rate of nitration is faster in concentrated nitric acid. The regioselectivity of the nitration (o-, p-, and m-selectivity) using different nitrating agents has been discussed elsewhere (Ref.2).

When only the fuming nitric acid in the solvent is used, the nitration starts due to the autoprotonation of nitric acid and generation of a nitronium cation $\ce{NO2+}$ (Ref.3):

$$\ce{HNO3 + HNO3 <=> H2NO3+ + NO3- <=> NO2+ + + H2O + NO3-} \tag4$$

The extended details of nitration of aromatics including anisole are given in Ref.4.

References:

1. David J. Belson, "Kinetics of nitration of anisole in aqueous nitric acid," Ind. Eng. Chem. Res. 1991, 30(7), 1485–1488 (DOI: https://doi.org/10.1021/ie00055a013).
2. George A. Olah, Henry C. Lin, Judith A. Olah, and Subhash C. Narang, "Variation of isomer distribution in electrophilic nitration of toluene, anisole, and o-xylene: Independence of high regioselectivity from reactivity of reagent," Proc. Natl. Acad. Sci. U S A 1978, 75(2), 545–548 (DOI: https://doi.org/10.1073/pnas.75.2.545).
3. Joanna Adamiak, "Controlled nitration of anisole over $\ce{HNO3/PO4/MoO3/SiO2/solvent}$ systems," Journal of Molecular Catalysis A: Chemical 2015, 407, 81–86 (DOI: https://doi.org/10.1016/j.molcata.2015.06.025).
4. J. G. Hoggett, R. B. Moodie, J. R. Penton, and K. Schofield, In Nitration and Aromatic Reactivity; Cambridge University Press: London, United Kingdom, 1971 (ISBN: 0-521-08029-0; ISBN 978-0521080293).

Yes, it is possible to nitrate anisole with just nitric acid. Following is the excerpt from a 1948 paper:

The nitration of anisole leads to formation of a mixture of nitroanisoles and nitrophenols in proportions depending on conditions. It is here shown that nitration of anisole in dilute nitric acid solution is nitrite-catalyzed and that the nitroanisoles are probable the intermediates in the reaction.

[...]

More precisely, anisole have been found to react rapidly with 40-50% nitric acid containing a little nitrous acid, but fails during many hours to react with nitric acid containing urea. The principal products when 40% nitric acid is used is nitrophenols; when more concentrated (60% nitric acid) used, then the principal product are nitroanisoles. The quantitative results were reported in table I:

They went ahead and tried to nitrate substituted anisoles e.g. p-nitroanisole

Ref.: The Mechanism of the Nitration of Anisole, R. M. Schramm and F. H. Westheimer, Journal of the American Chemical Society 1948 70 (5), 1782-1784 DOI: 10.1021/ja01185a036